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Multilevel time series (MTS) models are applied to estimate trends in time series of antenatal care coverage at several administrative levels in Bangladesh, based on repeated editions of the Bangladesh Demographic and Health Survey (BDHS) within the period 1994-2014. MTS models are expressed in an hierarchical Bayesian framework and fitted using Markov Chain Monte Carlo simulations. The models account for varying time lags of three or four years between the editions of the BDHS and provide predictions for the intervening years as well. It is proposed to apply cross-sectional Fay-Herriot models to the survey years separately at district level, which is the most detailed regional level. Time series of these small domain predictions at the district level and their variance-covariance matrices are used as input series for the MTS models. Spatial correlations among districts, random intercept and slope at the district level, and different trend models at district level and higher regional levels are examined in the MTS models to borrow strength over time and space. Trend estimates at district level are obtained directly from the model outputs, while trend estimates at higher regional and national levels are obtained by aggregation of the district level predictions, resulting in a numerically consistent set of trend estimates.

Multilevel time series (MTS) models are applied to estimate trends in time series of antenatal care coverage at several administrative levels in Bangladesh, based on repeated editions of the Bangladesh Demographic and Health Survey (BDHS) within the period 1994-2014. MTS models are expressed in an hierarchical Bayesian framework and fitted using Markov Chain Monte Carlo simulations. The models account for varying time lags of three or four years between the editions of the BDHS and provide predictions for the intervening years as well. It is proposed to apply cross-sectional Fay-Herriot models to the survey years separately at district level, which is the most detailed regional level. Time series of these small domain predictions at the district level and their variance-covariance matrices are used as input series for the MTS models. Spatial correlations among districts, random intercept and slope at the district level, and different trend models at district level and higher regional levels are examined in the MTS models to borrow strength over time and space. Trend estimates at district level are obtained directly from the model outputs, while trend estimates at higher regional and national levels are obtained by aggregation of the district level predictions, resulting in a numerically consistent set of trend estimates.

[Abstract]: This paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit-level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces. Generalitat Valenciana; Prometeo/2021/063 Ministerio de Ciencia e Innovación; PGC2018-096840- B-I00 Ministerio de Ciencia e Innovación; PID2020- 113578RB-I00 Xunta de Galicia; ED431G 2019/01 Xunta de Galicia; ED431C 2020/14 Xunta de Galicia; COV20/00604

Spatially disaggregated income indicators are typically estimated by using model-based methods that assume access to auxiliary information from population micro-data. In many countries like Germany and the UK population micro-data are not publicly available. In this work we propose small area methodology when only aggregate population-level auxiliary information is available. We use data-driven transformations of the response to satisfy the parametric assumptions of the used models. In the absence of population micro-data, appropriate bias-corrections for small area prediction are needed. Under the approach we propose in this paper, aggregate statistics (means and covariances) and kernel density estimation are used to resolve the issue of not having access to population micro-data. We further explore the estimation of the mean squared error using the parametric bootstrap. Extensive model-based and design-based simulations are used to compare the proposed method to alternative methods. Finally, the proposed methodology is applied to the 2011 Socio-Economic Panel and aggregate census information from the same year to estimate the average income for 96 regional planning regions in Germany.

In statistical modeling, it is crucial to have consistent variables that are the most relevant to the outcome variable(s) of interest in the model. With the increasing richness of data from multiple sources, the size of the pool of potential variables is escalating. Some variables, however, could provide redundant information, add noise to the estimation, or waste the degrees of freedom in the model. Therefore, variable selection is needed as a parsimonious process that aims to identify a minimal set of covariates for maximum predictive power. This study illustrated the variable selection methods considered and used in the small area estimation (SAE) modeling of measures related to the proficiency of adult competency that were constructed using survey data collected in the first cycle of the PIAAC. The developed variable selection process consisted of two phases: phase 1 identified a small set of variables that were consistently highly correlated with the outcomes through methods such as correlation matrix and multivariate LASSO analysis; phase 2 utilized a k-fold cross-validation process to select a final set of variables to be used in the final SAE models.

Permintaan estimasi pada level area kecil semakin meningkat, sedangkan keberhasilan pendugaan menggunakan metode tidak langsung dalam menurunkan RSE sangat bergantung pada kondisi data dan pemilihan metode yang tepat. Penelitian ini bertujuan untuk membandingkan hasil pendugaan persentase penduduk miskin menggunakan metode EBLUP dan HB Beta dalam menurunkan RSE hasil pendugaan langsung menggunakan studi kasus data kemiskinan level kecamatan Provinsi Jawa Timur. Data yang digunakan yaitu Susenas 2019 dan Podes 2019. Teknik clustering digunakan untuk mengestimasi beberapa kecamatan yang tidak tersampel dalam Susenas 2019. Distribusi prior yang digunakan pada metode SAE HB di penelitian ini adalah distribusi Beta. Hasilnya, metode EBLUP dan HB dapat mengatasi pendugaan pada area yang tidak tersampel dengan memanfaatkan informasi cluster. Selain itu, baik metode SAE EBLUP maupun HB mampu menurunkan nilai rata-rata dan median dari RSE hasil estimasi jika dibandingkan dengan pendugaan langsung. Dari 173 kecamatan hasil pendugaan langsung yang memiliki RSE >50%, metode EBLUP dapat mereduksinya menjadi 116 kecamatan. Sedangkan, metode HB mampu menurun RSE seluruh kecamatan menjadi dibawah 50%. Sehingga, dapat disimpulkan bahwa metode HB mampu memperbaiki hasil estimasi langsung lebih baik dari metode EBLUP pada pendugaan persentase penduduk miskin level kecamatan Provinsi Jawa Timur tahun 2019.

In many countries, HIV infections among MSM (MSMHIV) are closely monitored, and updated epidemiological reports are made available annually, yet the true prevalence of MSMHIV can be masked for areas with small population density or lack of data. Therefore, this study aimed to investigate the feasibility of small area estimation with a Bayesian approach to improve HIV surveillance. Data from the European MSM Internet Survey 2017 (EMIS-2017, Dutch subsample, n=3,459) and the Dutch survey ‘Men & Sexuality-2018’ (SMS-2018, n=5,653) were utilized in this study. We first applied a frequentist calculation to compare the observed relative risk of MSMHIV per Public Health Services (GGD) region in the Netherlands. We then applied a Bayesian spatial analysis and ecological regression to account for variance due to space and determinants associated with HIV among MSM to obtain more robust estimates. Results of the prevalence and risk estimations from EMIS-2017 and SMS-2018 converged with minor differences. Both estimations confirmed that the risk of MSMHIV is heterogenous across the Netherlands with some GGD regions, such as GGD Amsterdam [RR=1.21 (95% credible interval 1.05-1.38) by EMIS-2017; RR=1.39 (1.14-1.68) by SMS-2018], having a higher-than-average risk. Results from our ecological regression modelling revealed significant regional determinants which can impact on the risk for MSMHIV. In sum, our Bayesian approach to assess the risk of HIV among MSM was able to close data gaps and provide more robust prevalence and risk estimations. It is feasible and directly applicable for future HIV surveillance as a statistical adjustment tool.

INTRODUCTION: In France, oral pre-exposure prophylaxis (PrEP) for HIV prevention has been publicly available since 2016, mainly targeting at men who have sex with men (MSM). Reliable and robust estimations of the actual PrEP uptake among MSM on a localized level can provide additional insights to identify and better reach marginalized MSM within current HIV prevention service provision. This study used national pharmaco-epidemiology surveillance data and regional MSM population estimations to model the spatio-temporal distribution of PrEP uptake among MSM in France 2016-2021 to identify marginalized MSM at risk for HIV and increase their PrEP uptake. METHODS: We first applied Bayesian spatial analyses with survey-surveillance-based HIV incidence data as a spatial proxy to estimate the size of (1) regional HIV-negative MSM populations and (2) MSM who could be eligible for PrEP use according to French PrEP guidelines. We then applied Bayesian spatio-temporal ecological regression modelling to estimate the regional prevalence and relative probability of the overall- and new-PrEP uptake from 2016 to 2021 across France. RESULTS: HIV-negative and PrEP-eligible MSM populations vary regionally across France. Île-de-France was estimated to have the highest MSM density compared to other French regions. According to the final spatio-temporal model, the relative probability of overall PrEP uptake was heterogeneous across France but remained stable over time. Urban areas have higher-than-average probabilities of PrEP uptake. The prevalence of PrEP use increased steadily (ranging from 8.8% [95% credible interval 8.5%;9.0%] in Nouvelle-Aquitaine to 38.2% [36.5%;39.9%] in Centre-Val-de-Loire in 2021). CONCLUSIONS: Our results show that using Bayesian spatial analysis as a novel methodology to estimate the localized HIV-negative MSM population is feasible and applicable. Spatio-temporal models showed that despite the increasing prevalence of PrEP use in all regions, geographical disparities and inequalities of PrEP uptake continued to exist over time. We identified regions that would benefit from greater tailoring and delivery efforts. Based on our findings, public health policies and HIV prevention strategies could be adjusted to better combat HIV infections and to accelerate ending the HIV epidemic.

In spite of its high practical relevance, cluster specific multiple inference for linear mixed model predictors has hardly been addressed so far. While marginal inference for population parameters is well understood, conditional inference for the cluster specific predictors is more intricate. This work introduces a general framework for multiple inference in linear mixed models for cluster specific predictors. Consistent confidence sets for multiple inference are constructed under both, the marginal and the conditional law. Furthermore, it is shown that, remarkably, corresponding multiple marginal confidence sets are also asymptotically valid for conditional inference. Those lend themselves for testing linear hypotheses using standard quantiles without the need of re-sampling techniques. All findings are validated in simulations and illustrated along a study on Covid-19 mortality in US state prisons., 31 pages, 4 figures

The Household Pulse Survey, recently released by the U.S. Census Bureau, gathers information about the respondents’ experiences regarding employment status, food security, housing, physical and mental health, access to health care, and education disruption. Design-based estimates are produced for all 50 states and the District of Columbia (DC), as well as 15 Metropolitan Statistical Areas (MSAs). Using public-use microdata, this paper explores the effectiveness of using unit-level model-based estimators that incorporate spatial dependence for the Household Pulse Survey. In particular, we consider Bayesian hierarchical model-based spatial estimates for both a binomial and a multinomial response under informative sampling. Importantly, we demonstrate that these models can be easily estimated using Hamiltonian Monte Carlo through the Stan software package. In doing so, these models can readily be implemented in a production environment. For both the binomial and multinomial responses, an empirical simulation study is conducted, which compares spatial and non-spatial models. Finally, using public-use Household Pulse Survey micro-data, we provide an analysis that compares both design-based and model-based estimators and demonstrates a reduction in standard errors for the model-based approaches.

This dissertation consists of four empirical chapters on inequality, with Chapters 1 and 2 focusing on regional inequality, and Chapters 3 and 4 examining the origins of inequality at the individual level. The first chapter makes a methodological contribution to the literature on inequality across regions by providing the fayherriot command for the statistical software Stata. The command implements the Fay-Herriot model (Fay and Herriot, 1979), a small-area estimation technique (Rao and Molina, 2015) that improves the precision of region-level direct estimates using region-level covariates. The command implements the default model and encompasses additional options to a) produce out-of-sample predictions, b) adjust non-positive random effects variance estimates, and c) deal with the violation of model assumptions. An application of the command in the last part of the chapter shows that the statistical precision of regional income estimates can be considerably improved, allowing for a more robust examination of inequality between regions. Similar to the first chapter, the second chapter is concerned with providing improved data for the analysis of regional differences. For this purpose, the chapter presents a novel regional database of tax revenues for the interwar period in Germany. The database contains annual income and payroll, corporate, wealth, and turnover tax revenues for 900 tax districts in the former German Empire over the period 1926 to 1938. Moreover, the database provides geocoded borders for each tax district and year, allowing researchers to flexibly link the tax data to other geocoded data sources. The use of the data is further facilitated by a detailed description of the interwar German tax system in the second part of the chapter. Comparing the tax data with historical regional GDP estimates, the chapter finds high correlations, suggesting that tax data are valid proxy for regional economic development and a useful data source for regional analyses. The third chapter focuses on individual inequality and one of the largest shocks to private wealth in 20th century Germany: the destruction of the housing stock during the Second World War. By the end of the war, an estimated \num{20} percent of the West German housing stock had been destroyed, and the chapter examines the extent to which regional differences in destruction can explain differences in private wealth today. As the empirical basis, the analysis links a unique dataset on the levels of wartime destruction in 1739 West German cities with recent micro data on household wealth provided by the German Socio-Economic Panel (SOEP). The results indicate that wealth is still significantly lower today among individuals born in cities or villages that were badly damaged. Similarly, the destruction of parents’ cities or villages of birth has significant negative effects on the wealth of their descendants. These detrimental effects are robust after controlling for a rich set of pre-war regional and city-level control variables. In a complementary mediation analysis, the chapter studies potential channels such as health, education, and work experience, through which the wartime destruction could have affected wealth accumulation. The fourth chapter investigates wealth inequality between migrants and natives in Germany. In particular, the chapter examines the role of characteristics and behavior for the development of the large wealth gaps between the two groups. Based on data from the SOEP, the results of this chapter show that the native-migrant wealth gap is large and persistent throughout the 2002 to 2017 period. A subsequent decomposition analysis exploits the panel dimension of the data and shows that working-age migrants cannot significantly catch up with natives in terms of net wealth because they lack sufficient levels of income, inheritances, and inter-vivos gifts. The results also indicate that especially native individuals consume, transfer, or lose significant amounts of wealth over time, which reduces the pace at which the wealth inequality between migrants and natives increases., Diese Dissertation setzt sich aus vier empirischen Kapiteln über Ungleichheit zusammen, wobei die Kapitel 1 und 2 regionale Ungleichheiten behandeln, während die Kapitel 3 und 4 Ungleichheit auf individueller Ebene untersuchen. Das erste Kapitel leistet einen methodischen Beitrag zur Literatur über regionale Ungleichheit, indem es den Befehl fayherriot für die Statistiksoftware Stata bereitstellt. Der Befehl implementiert das Fay-Herriot-Modell (Fay and Herriot, 1979), eine Small-Area-Methode (Rao and Molina, 2015), die die Genauigkeit direkter Schätzungen auf regionaler Ebene unter Verwendung von regionaler Kovariate verbessert. Der Befehl implementiert das Standardmodell und umfasst zusätzliche Optionen, um a) Out-of-Sample-Vorhersagen zu treffen, b) nichtpositive Schätzungen der Fehlertermvarianz zu korrigieren und c) mit weiteren Verletzung von Modellannahmen umzugehen. Eine Anwendung des Befehls im letzten Teil des Kapitels zeigt, dass das Fay-Herriot-Modell die statistische Genauigkeit von regionalen Einkommensschätzungen erheblich verbessern kann, was eine robustere Untersuchung der Ungleichheit zwischen Regionen ermöglicht. Ähnlich wie das erste Kapitel hat das zweite Kapitel das Ziel, die Datengrundlage für die Analyse regionaler Unterschiede zu verbessern. Zu diesem Zweck wird in dem Kapitel eine neue regionale Datenbank mit Steuereinnahmen aus der Zwischenkriegszeit in Deutschland bereit- und vorgestellt. Die Datenbank enthält die jährlichen Steuereinnahmen aus der Einkommen- , Körperschaft-, Vermögen- und Umsatzsteuer sowie die des Lohnsteuerabzugs für die rund 900 Finanzämter im ehemaligen Deutschen Reich im Zeitraum von 1926 bis 1938. Darüber hinaus bietet die Datenbank geocodierte Grenzen für jedes Jahr und jeden Finanzamtsbezirk, so dass die Steuerdaten flexibel mit anderen geocodierten Datenquellen verknüpft werden können. Um die Datennutzung weiter zu erleichtern, ist im zweiten Teil des Kapitels eine detaillierte Beschreibung des deutschen Steuersystems der Zwischenkriegszeit enthalten. Beim Vergleich der Steuerdaten mit Schätzungen für das regionale, historische Bruttoinlandsprodukt werden hohe Korrelationen festgestellt, was darauf hindeutet, dass die Steuerdaten ein gültiger Proxy für die regionale Wirtschaftsentwicklung und eine nützliche Datenquelle für regionale Analysen sind. Das dritte Kapitel behandelt Ungleichheiten zwischen Personen und analysiert einen der größten Schocks für das Privatvermögen in Deutschland im 20. Jahrhundert: die Zerstörung des Wohnungsbestands während des Zweiten Weltkriegs. Bei Kriegsende waren schätzungsweise 20 Prozent des westdeutschen Wohnungsbestands zerstört, und in diesem Kapitel wird untersucht, inwieweit regionale Unterschiede bei der Zerstörung Unterschiede im heutigen Privatvermögen erklären können. Als empirische Grundlage verknüpft die Analyse einen detaillierten Datensatz über das Ausmaß der Kriegszerstörungen in 1739 westdeutschen Städten mit aktuellen Mikrodaten zum Vermögen privater Haushalte aus dem Sozio-oekonomischen Panel (SOEP). Die Ergebnisse zeigen, dass das Vermögen von Personen, die in stark zerstörten Städten oder Dörfern geboren wurden, auch heute noch deutlich geringer ist. Ebenso hat die Zerstörung der Geburtsorte der Eltern signifikante negative Auswirkungen auf das heutige Vermögen ihrer Nachkommen. Die geschätzten Effekte sind robust auch nachdem für eine Reihe von Variablen auf regionaler und städtischer Ebene aus der Vorkriegszeit kontrolliert wird. In einer ergänzenden Mediationsanalyse werden in diesem Kapitel mögliche Wirkungskanäle wie Gesundheit, Bildung und Berufserfahrung untersucht, über die die Kriegszerstörung die Vermögensbildung beeinflusst haben könnte. Das vierte Kapitel untersucht die Vermögensungleichheit zwischen Zugewanderten und Einheimischen in Deutschland. Insbesondere untersucht das Kapitel die Bedeutung von Merkmalsunterschieden für die Entwicklung der Vermögensunterschiede zwischen den beiden Gruppen. Auf Grundlage von Daten des SOEP zeigen die Ergebnisse dieses Kapitels, dass das Vermögensgefälle zwischen Einheimischen und Zugewanderten sehr groß und über den gesamten Analysezeitraum von 2002 bis 2017 relativ stabil ist. Eine anschließende Dekompositionsanalyse nutzt die Paneldimension der Daten aus und zeigt, dass Zugewanderte im erwerbsfähigen Alter hinsichtlich des Nettovermögens über die Zeit nicht wesentlich zur einheimischen Bevölkerung aufschließen können, da sie nicht über das ausreichende Einkommen verfügen und nicht im gleichen Maße von Erbschaften oder Schenkungen profitieren. Die Ergebnisse deuten außerdem darauf hin, dass vor allem einheimische Personen im Laufe der Zeit signifikante Teile ihres Vermögens aufzehren, übertragen oder verlieren, wodurch sich die Geschwindigkeit verringert, mit der die Vermögensungleichheit zwischen Zugewanderten und Einheimischen zunimmt.

In this paper we estimate monetary and non-monetary poverty measures at two sub-regional levels in the region of Tuscany (Italy) using data from the ad-hoc Survey on Vulnerability and Poverty held by Regional Institute from Economic Planning of Tuscany (IRPET). We estimate the percentage of households living in poverty conditions and three supplementary fuzzy measures of poverty regarding deprivation in basic needs and lifestyle, children deprivation, and financial insecurity. The key feature of the survey is that it was carried out after the COVID-19 pandemic, therefore, some of the items collected focus on the subjective perception of poverty eighteen months after the beginning of the pandemic. We assess the quality of these estimates either with initial direct estimates along with their sampling variance, and with a secondary small area estimation when the formers are not sufficiently accurate.

When data analysts use linear mixed models, they usually encounter two practical problems: (a) the true model is unknown and (b) the Gaussian assumptions of the errors do not hold. While these problems commonly appear together, researchers tend to treat them individually by (a) finding an optimal model based on the conditional Akaike information criterion (cAIC) and (b) applying transformations on the dependent variable. However, the optimal model depends on the transformation and vice versa. In this paper, we aim to solve both problems simultaneously. In particular, we propose an adjusted cAIC by using the Jacobian of the particular transformation such that various model candidates with differently transformed data can be compared. From a computational perspective, we propose a step-wise selection approach based on the introduced adjusted cAIC. Model-based simulations are used to compare the proposed selection approach to alternative approaches. Finally, the introduced approach is applied to Mexican data to estimate poverty and inequality indicators for 81 municipalities.

For evidence-based policy-making, reliable information on socio-economic indicators are essential. Sample surveys have a long tradition of providing cost-efficient information on these indicators. Mostly, there is a demand for the quantity of interest not only at the level of the total population, but especially at the level of sub-populations (geographic areas or sociodemographic groups) called areas or domains. To gain insights into these sub-populations, disaggregated direct estimators can be used, which are calculated solely on area-specific survey data. An area is regarded as ’large’ if the sample size is large enough to enable reliable direct estimates. If the precision of the direct estimates is not sufficient or the sample size is even zero, the area is considered as ’small’. This is particularly common at high spatial or socio-demographic resolutions. Small area estimation (SAE) is promising to overcome this problem without the need for larger and thus more costly surveys. The essence of SAE techniques is that they ’borrow strength’ from other areas to improve their predictions. For this purpose, a model is built on survey data that links additional auxiliary data and exploits area-specific structures. Suitable auxiliary data sources are administrative and register data, such as the census. In many countries, such data are strictly protected by confidentiality agreements and access to population micro-data is a challenge even for gatekeeper organisations. Thus, users have an increased interest in SAE estimators that do not require population micro-data to serve as auxiliary data. In this thesis, new methods in the absence of population micro-data are presented and applications on socio-economic highly relevant indicators are demonstrated. Since different SAE models impose different data requirements, Part I bundles research combining unit-level survey data and limited auxiliary data, e.g., aggregated data such as means, which is a common data situation for users. To account for the unit-level survey information the use of the well-known nested error regression (NER) model is targeted. This model is a special case of a linear mixed model based on several assumptions. But how can users proceed if the model assumptions are not fulfilled? In Part I, this thesis provides two new approaches to deal with this issue. One promising approach is to transform the response. Since several socio-economically relevant variables, such as income, have a skewed distribution, the log-transformation of the response is an established way to meet the assumptions. However, the data-driven log-shift transformation is even more promising because it extends the log by an additional parameter and achieves more flexibility. Chapter 1 introduces both transformations in the absence of population micro-data. A particular challenge is the transformation of the small area means back to the original scale. Hence, the proposed approach introduces aggregate statistics (means and covariances) and kernel density estimation to resolve the issue of lacking population micro-data. Uncertainty estimation is developed, and all methods are evaluated in design- and model-based settings. The proposed method is applied to estimate regional income in Germany using the Socio-Economic Panel and census data. It achieves a clear improvement in reliability, and thus demonstrates the importance of the method. To conveniently enable further applications, this new methodology is implementedin the R package saeTrafo. Chapter 2 describes the various functionalities of the package using publicly available income data. To increase user-friendliness, established unit-level models under transformations and their uncertainty estimations are implemented and the most suitable method is automatically selected. For some applications, however, it is challenging to find a suitable transformation or, more generally, to specify a model, particularly in the presence of complex interactions. For this case, machine learning methods are valuable as a transformation is not necessarily required nor a model needs to be explicitly specified. The semi-parametric framework of mixed effects random forest (MERF) combines the advantages of random forests (robustness against outliers and implicit model-selection) with the ability to model hierarchical dependencies as present in SAE approaches. Chapter 3 introduces MERFs in the absence of population micro-data. As existing random forest algorithm require unit-level auxiliary population data, an alternative strategy is introduced. It adaptively incorporates aggregated auxiliary information through calibration-weights to circumvent unit-level auxiliary data. Applying the proposed method on opportunity costs of care work for Germany using the Socio-Economic Panel and census data demonstrates the gain in accuracy in comparison to both direct estimates and the classical NER model. In contrast to methods using a unit-level sample survey, Part II focuses on the well-known class of area-level SAE models requiring direct estimates from a survey while using (once again) only aggregated population auxiliary data. This thesis presents two particularly relevant applications of this model class. Chapter 4 examines regional consumer price indices (CPIs) in the United Kingdom (UK), contributing to the great interest in monitoring inflation at the spatial level. The SAE challenge is to construct model-based expenditure weights to generate the regional basket of goods and services for the twelve regions of the UK. They are estimated and constructed from the living cost and food survey. Furthermore, available price data are linked to the SAE estimated baskets to produce regional CPIs. The resulting CPI series are closely examined, and smoothing techniques are applied. As a result, the reliability improves, but the CPI series are still too volatile for policy use. However, our research serves as a valuable framework for the creation of a regional CPI in the future. The second application also explores the reliability of the disaggregated estimation of a politically and economically highly relevant indicator, in this case the unemployment rate. The regional target level are the functional urban areas in the German federal state North Rhine-Westphalia. In Chapter 5, two types of unemployment rates - the traditional one and an alternative definition taking commuting into account - are estimated and compared. Direct estimates from the labour force survey are linked with SAE methods to passively collected mobile network data. This alternative data source is real-time available, offers spatial flexible resolutions, and is dynamic. In compliance with data protection rules, we obtain aggregated auxiliary mobile network information from the data provider. The SAE methods improve the reliability, and the resulting predictions show that alternative unemployment rates in German city cores are lower than traditional estimated official unemployment rates indicate.

The thesis combines four papers that introduce a coherent framework based on MERFs for the estimation of spatially disaggregated economic and inequality indicators and associated uncertainties. Chapter 1 focusses on flexible domain prediction using MERFs. We discuss characteristics of semi-parametric point and uncertainty estimates for domain-specific means. Extensive model- and design-based simulations highlight advantages of MERFs in comparison to 'traditional' LMM-based SAE methods. Chapter 2 introduces the use of MERFs under limited covariate information. The access to population-level micro-data for auxiliary information imposes barriers for researchers and practitioners. We introduce an approach that adaptively incorporates aggregated auxiliary information using calibration-weights in the absence of unit-level auxiliary data. We apply the proposed method to German survey data and use aggregated covariate census information from the same year to estimate the average opportunity cost of care work for 96 planning regions in Germany. In Chapter 3, we discuss the estimation of non-linear poverty and inequality indicators. Our proposed method allows to estimate domain-specific cumulative distribution functions from which desired (non-linear) poverty estimators can be obtained. We evaluate proposed point and uncertainty estimators in a design-based simulation and focus on a case study uncovering spatial patterns of poverty for the Mexican state of Veracruz. Additionally, Chapter 3 informs a methodological discussion on differences and advantages between the use of predictive algorithms and (linear) statistical models in the context of SAE. The final Chapter 4 complements the previous research by implementing discussed methods for point and uncertainty estimates in the open-source R package SAEforest. The package facilitates the use of discussed methods and accessibly adds MERFs to the existing toolbox for SAE and official statistics. Overall, this work aims to synergize aspects from two statistical spheres (e.g. 'traditional' parametric models and nonparametric predictive algorithms) by critically discussing and adapting tree-based methods for applications in SAE. In this perspective, the thesis contributes to the existing literature along three dimensions: 1) The methodological development of alternative semi-parametric methods for the estimation of non-linear domain-specific indicators and means under unit-level and aggregated auxiliary covariates. 2) The proposition of a general framework that enables further discussions between 'traditional' and algorithmic approaches for SAE as well as an extensive comparison between LMM-based methods and MERFs in applications and several model and design-based simulations. 3) The provision of an open-source software package to facilitate the usability of methods and thus making MERFs and general SAE methodology accessible for tailored research applications of statistical, institutional and political practitioners.

[Abstract]: This paper investigates the small area estimation of population averages of unit-level compositional data. The new methodology transforms the compositions into vectors of Rm and assumes that the vectors follow a multivariate nested error regression model. Empirical best predictors of domain indicators are derived from the fitted model, and their mean squared errors are estimated by parametric bootstrap. The empirical analysis of the behavior of the introduced predictors is investigated by means of simulation experiments. An application to real data from the Spanish household budget survey is given. The target is to estimate the average of proportions of annual household expenditures on food, housing and others, by Spanish provinces. Generalitat Valenciana; Prometeo/2021/063 Xunta de Galicia; ED431C 2020/14 Xunta de Galicia; ED431G 2019/01 Axencia Galega de Innovación; COV20/00604 Supported by the Instituto Galego de Estatística, by the Grants PGC2018-096840-B-I00 and PID2020-113578RB-I00 of the Spanish Ministerio de Economía y Competitividad, by the Grant Prometeo/2021/063 of the Generalitat Valenciana, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C 2020/14), and by GAIN (Galician Innovation Agency) and the Regional Ministry of Economy, Employment and Industry Grant COV20/00604 and Centro de Investigación del Sistema Universitario de Galicia ED431G 2019/01, all of them through the ERDF.

Quantitative sociologists and social policymakers are increasingly interested in local context. Some city-specific studies have developed new primary data collection efforts to analyze inequality at the neighborhood level, but methods from spatial microsimulation have yet to be broadly used in sociology to take better advantage of existing public data sets. The American Community Survey (ACS) is the largest household survey in the United States and indispensable for detailed analysis of specific places and populations. The authors propose a technique, tree-based spatial microsimulation, to produce “small-area” (census-tract) estimates of any person- or household-level phenomenon that can be derived from ACS microdata variables. The approach is straightforward and computationally efficient, based only on publicly available data, and it provides more reliable estimates than do prevailing methods of microsimulation. The authors demonstrate the technique’s capabilities by producing tract-level estimates, stratified by race/ethnicity, of (1) the proportion of people in the census-tract population who have children and work in an essential occupation and (2) the proportion of people in the census-tract population living below the federal poverty threshold and in a household that spends greater than 50 percent of monthly income on rent or owner costs. These examples are relevant to understanding the sociospatial inequalities dramatized by the coronavirus disease 2019 pandemic. The authors discuss potential extensions of the technique to derive small-area estimates of variables observed in surveys other than the ACS.

In the Netherlands, very precise and detailed statistical information on labour force participation is derived from registers. A drawback of this data source is that it is not timely since definitive versions typically become available with a delay of two years. More timely information on labour force participation can be derived from the Labour Force Survey (LFS). Quarterly figures, for example, become available six weeks after the calendar quarter. A well-known drawback of this data source is the uncertainty due to sampling error. In this article, a nowcast method is proposed to produce preliminary but timely nowcasts for the register labour force participation on a quarterly frequency at the level of municipalities and neighbourhoods, using the data from the LFS. As a first step, small area estimates for quarterly municipal figures on labour force participation are obtained using the LFS data and the unit-level modelling approach of Battese, Harter and Fuller (1988). Subsequently, time series of these small area estimates at the municipal level are combined with time series on register labour force participation in a bivariate structural time series model in order to nowcast the register labour force participation at the level of municipalities and neighbourhoods.

Socioeconomic indicators play a crucial role in monitoring political actions over time and across regions. Income-based indicators such as the median income of sub-populations can provide information on the impact of measures, e.g., on poverty reduction. Regional information is usually published on an aggregated level. Due to small sample sizes, these regional aggregates are often associated with large standard errors or are missing if the region is unsampled or the estimate is simply not published. For example, if the median income of Hispanic or Latino Americans from the American Community Survey is of interest, some county-year combinations are not available. Therefore, a comparison of different counties or time-points is partly not possible. We propose a new predictor based on small area estimation techniques for aggregated data and bivariate modeling. This predictor provides empirical best predictions for the partially unavailable county-year combinations. We provide an analytical approximation to the mean squared error. The theoretical findings are backed up by a large-scale simulation study. Finally, we return to the problem of estimating the county-year estimates for the median income of Hispanic or Latino Americans and externally validate the estimates.

Small area estimation (SAE) methods can provide information that conventional direct survey estimation methods cannot. The use of small area estimates based on linear and generalized linear mixed models is still very limited, possibly because of the perceived complexity of estimating the root mean square errors (RMSEs) of the estimates. This paper outlines a study used to determine the conditions under which the estimated RMSEs, produced as part of statistical output (‘plug-in’ estimates of RMSEs) could be considered appropriate for a practical application of SAE methods where one of the main requirements was to use SAS software. We first show that the estimated RMSEs created using an EBLUP model in SAS and those obtained using a parametric bootstrap are similar to the published estimated RMSEs for the corn data in the seminal paper by Battese, Harter and Fuller. We then compare plug-in estimates of RMSEs from SAS procedures used to create EBLUP and EBP estimators against estimates of RMSEs obtained from a parametric bootstrap. For this comparison we created estimates of current smoking in males for 153 local government areas (LGAs) using data from the NSW Population Health Survey in Australia. Demographic variables from the survey data were included as covariates, with LGA-level population proportions, obtained mainly from the Australian Census used for prediction. For the EBLUP, the estimated plug-in estimates of RMSEs can be used, provided the sample size for the small area is more than seven. For the EBP, the plug-in estimates of RMSEs are suitable for all in-sample areas, out-of-sample areas need to use estimated RMSEs that use the parametric bootstrap.

Metode Small Area Estimations (SAE) digunakan sebagai pendekatan yang reliabel dalam mengatasi kendala ketidakcukupan sampel pada survei sampel. BPS memproduksi statistik area kecil menggunakan metode SAE popular seperti Empirical Best Linear Unbiased Prediction dalam model Fay-Herriot (EBLUP-FH). Metode EBLUP-FH sebagai pendekatan parametrik memerlukan asumsi normalitas dan terbebas dari outliers pada kedua komponen random effect-nya. Namun, hal tersebut sulit dipenuhi karena seringkali data di lapangan berperilaku ekstrim. Metode SAE M-quantile Chambers-Dunstan (CD) merelaksasi asumsi parametrik dan robust dalam inferensi terhadap outliers. Penelitian ini mengkaji metode M-quantile CD dalam meningkatkan robustness pendugaan area kecil melalui penerapannya pada data riil untuk estimasi rata-rata pengeluaran rumah tangga per kapita tingkat kecamatan di DI Yogyakarta tahun 2018. Penelitian ini menggunakan data Susenas 2018 dan Podes 2018. Hasil implementasi pada data riil menunjukkan model M-quantile CD berhasil memperbaiki presisi EBLUP-FH. Dengan mengimplementasikan M-quantile CD diharapkan estimasi data berperilaku ekstrim lebih akurat untuk pengambilan kebijakan di daerah.

Multilevel time series (MTS) models are applied to estimate trends in time series of antenatal care coverage at several administrative levels in Bangladesh, based on repeated editions of the Bangladesh Demographic and Health Survey (BDHS) within the period 1994-2014. MTS models are expressed in an hierarchical Bayesian framework and fitted using Markov Chain Monte Carlo simulations. The models account for varying time lags of three or four years between the editions of the BDHS and provide predictions for the intervening years as well. It is proposed to apply cross-sectional Fay-Herriot models to the survey years separately at district level, which is the most detailed regional level. Time series of these small domain predictions at the district level and their variance-covariance matrices are used as input series for the MTS models. Spatial correlations among districts, random intercept and slope at the district level, and different trend models at district level and higher regional levels are examined in the MTS models to borrow strength over time and space. Trend estimates at district level are obtained directly from the model outputs, while trend estimates at higher regional and national levels are obtained by aggregation of the district level predictions, resulting in a numerically consistent set of trend estimates.

The tipsae package implements a set of small area estimation tools for mapping proportions and indicators defined on the unit interval. It provides for small area models defined at area level, including the classical Beta regression, Zero and/or One Inflated Beta and Flexible Beta ones, possibly accounting for spatial and/or temporal dependency structures. The models, developed within a Bayesian framework, are estimated through Stan language, allowing fast estimation and customized parallel computing. The additional features of the tipsae package, such as diagnostics, visualization and exporting functions as well as variance smoothing and benchmarking functions, improve the user experience through the entire process of estimation, validation and outcome presentation. A Shiny application with a user-friendly interface further eases the implementation of Bayesian models for small area analysis.

Angka Kematian Bayi (AKB) merupakan indikator yang penting karena dapat digunakan untuk membandingkan status kesehatan antar penduduk. Pendugaan AKB berdasarkan Survei Demografi dan Kesehatan Indonesia (SDKI) hanya berskala nasional atau provinsi namun dengan adanya sistem desentralisasi diperlukan prediksi untuk area yang lebih kecil seperti kabupaten/kota. Small Area Estimation (SAE) dapat digunakan untuk menduga AKB di tingkat kabupaten/kota, yaitu dengan menggunakan generalized linear mixed model. AKB merupakan data cacahan dengan peluang sangat kecil, sehingga diasumsikan mengikuti sebaran Poisson. Model Poisson memiliki asumsi rataan sama dengan ragam, tetapi asumsi ini sering terlanggar. Salah satu penyebabnya yaitu proporsi nilai nol yang sangat besar pada data (excess zero). Penelitian ini menggunakan Zero Inflated Poisson (ZIP) mixed model sebagai alternatif dari Poisson mixed model. Hasil perbandingan RMSE, ZIP mixed model jauh lebih baik dibandingkan Poisson mixed model serta dapat memperbaiki hasil dugaan langsung AKB.

Major depression is a severe mental disorder that is associated with strongly increased mortality. The quantification of its prevalence on regional levels represents an important indicator for public health reporting. In addition to that, it marks a crucial basis for further explorative studies regarding environmental determinants of the condition. However, assessing the distribution of major depression in the population is challenging. The topic is highly sensitive, and national statistical institutions rarely have administrative records on this matter. Published prevalence figures as well as available auxiliary data are typically derived from survey estimates. These are often subject to high uncertainty due to large sampling variances and do not allow for sound regional analysis. We propose a new area-level Poisson mixed model that accounts for measurement errors in auxiliary data to close this gap. We derive the empirical best predictor under the model and present a parametric bootstrap estimator for the mean squared error. A method of moments algorithm for consistent model parameter estimation is developed. Simulation experiments are conducted to show the effectiveness of the approach. The methodology is applied to estimate the major depression prevalence in Germany on regional levels crossed by sex and age groups.

This article proposes a new methodology for estimating the proportions of households that had experience of international migration at the municipal level in Colombia. The Colombian National Statistical Office usually produces estimations of internal migration based on the results of population censuses, but there is a lack of disaggregated information about the main small areas of origin of the population that emigrates from Colombia. The proposed methodology uses frequentist and Bayesian approaches based on a Fay-Herriot model and is illustrated by one example with a dependent variable from the Demographic and Health Survey 2015 and covariables available from the population census 2005. The proposed alternative produces proportion estimates that are consistent with sample sizes and the main internal immigration trends in Colombia. Additionally, the estimated coefficients of variation are lower than 20% for municipalities for both frequentist and Bayesian approaches and large demographically-relevant capital cities and therefore estimates may be considered to be reliable. Finally, we illustrate how the proposed alternative leads to important reductions of the estimated coefficients of variations for the areas with very small sample sizes.

Regional prevalence estimation requires the use of suitable statistical methods on epidemiologic data with substantial local detail. Small area estimation with medical treatment records as covariates marks a promising combination for this purpose. However, medical routine data often has strong internal correlation due to diagnosis-related grouping in the records. Depending on the strength of the correlation, the space spanned by the covariates can become rank-deficient. In this case, prevalence estimates suffer from unacceptable uncertainty as the individual contributions of the covariates to the model cannot be identified properly. We propose an area-level logit mixed model for regional prevalence estimation with a new fitting algorithm to solve this problem. We extend the Laplace approximation to the log-likelihood by an $$\ell _2$$ ℓ 2 -penalty in order to stabilize the estimation process in the presence of covariate rank-deficiency. Empirical best predictors under the model and a parametric bootstrap for mean squared error estimation are presented. A Monte Carlo simulation study is conducted to evaluate the properties of our methodology in a controlled environment. We further provide an empirical application where the district-level prevalence of multiple sclerosis in Germany is estimated using health insurance records.

Ibrahim Jahun,1 Emilio Dirlikov,2 Solomon Odafe,1 Aminu Yakubu,1 Andrew T Boyd,2 Pamela Bachanas,2 Charles Nzelu,3 Gambo Aliyu,4 Tedd Ellerbrock,2 Mahesh Swaminathan1 On behalf of CDC Nigeria ART Surge Team1US Centers for Disease Control and Prevention, Division of Global HIV and TB, Center for Global Health - Nigeria, Abuja Federal Capital Territory, Nigeria; 2US Centers for Disease Control and Prevention, Division of Global HIV and TB, Center for Global Health, Atlanta, GA, USA; 3Federal Ministry of Health (FMOH), Abuja, Nigeria; 4National Agency for the Control of AIDS (NACA), Abuja, Federal Capital Territory, NigeriaCorrespondence: Ibrahim JahunCenters for Disease Control and Prevention (CDC)-Nigeria, Embassy of the United States of America, Central Business District, Abuja, Federal Capital Territory, NigeriaTel +234 8037013715Email drjahun@yahoo.co.ukPurpose: The 2018 Nigeria HIV/AIDS Indicator and Impact Survey (NAIIS) showed Nigeria’s progress toward the UNAIDS 90-90-90 targets: 47% of HIV-positive individuals knew their status; of these, 96% were receiving antiretroviral therapy (ART); and of these, 81% were virally suppressed. To improve identification of HIV-positive individuals, Nigeria developed an Enhanced Community Case-Finding Package (ECCP). We describe ECCP implementation in nine states and assess its effect.Methods: ECCP included four core strategies (small area estimation [SAE] of people living with HIV [PLHIV], map of HIV-positive patients by residence, HIV risk-screening tool [HRST], and index testing [IT]) and four supportive strategies (alternative healthcare outlets, performance-based incentives for field testers, Project Extension for Community Healthcare Outcomes, and interactive dashboards). ECCP was deployed in nine of 10 states prioritized for ART scale-up. Weekly program data (October 2019–March 2020) were tracked and analyzed.Results: Of the total 774 LGAs in Nigeria, using SAE, 103 (13.3%) high-burden LGAs were identified, in which 2605 (28.0%) out of 9,294 hotspots were prioritized by mapping newly identified PLHIV by residential addresses. Over 22 weeks, among 882,449 individuals screened using HRST, 723,993 (82.0%) were eligible and tested for HIV (state range, 43.7– 90.4%), out of which 20,616 were positive. Through IT, an additional 3,724 PLHIV were identified. In total, 24,340 PLHIV were identified and 97.4% were linked to life-saving antiretroviral therapy. The number of newly identified PLHIV increased 17-fold over 22 weeks (week 1: 89; week 22: 1,632). Overall mean HIV positivity rate by state was 3.3% (range, 1.8– 6.4%).Conclusion: Using ECCP in nine states in Nigeria increased the number of PLHIV in the community who knew their status, allowing them to access life-saving care and decreasing the risk of HIV transmission.Keywords: ART Surge, small area estimation, HIV risk assessment tool, index partner testing

Ibrahim Jahun,1 Emilio Dirlikov,2 Solomon Odafe,1 Aminu Yakubu,1 Andrew T Boyd,2 Pamela Bachanas,2 Charles Nzelu,3 Gambo Aliyu,4 Tedd Ellerbrock,2 Mahesh Swaminathan1 On behalf of CDC Nigeria ART Surge Team1US Centers for Disease Control and Prevention, Division of Global HIV and TB, Center for Global Health - Nigeria, Abuja Federal Capital Territory, Nigeria; 2US Centers for Disease Control and Prevention, Division of Global HIV and TB, Center for Global Health, Atlanta, GA, USA; 3Federal Ministry of Health (FMOH), Abuja, Nigeria; 4National Agency for the Control of AIDS (NACA), Abuja, Federal Capital Territory, NigeriaCorrespondence: Ibrahim JahunCenters for Disease Control and Prevention (CDC)-Nigeria, Embassy of the United States of America, Central Business District, Abuja, Federal Capital Territory, NigeriaTel +234 8037013715Email drjahun@yahoo.co.ukPurpose: The 2018 Nigeria HIV/AIDS Indicator and Impact Survey (NAIIS) showed Nigeria’s progress toward the UNAIDS 90-90-90 targets: 47% of HIV-positive individuals knew their status; of these, 96% were receiving antiretroviral therapy (ART); and of these, 81% were virally suppressed. To improve identification of HIV-positive individuals, Nigeria developed an Enhanced Community Case-Finding Package (ECCP). We describe ECCP implementation in nine states and assess its effect.Methods: ECCP included four core strategies (small area estimation [SAE] of people living with HIV [PLHIV], map of HIV-positive patients by residence, HIV risk-screening tool [HRST], and index testing [IT]) and four supportive strategies (alternative healthcare outlets, performance-based incentives for field testers, Project Extension for Community Healthcare Outcomes, and interactive dashboards). ECCP was deployed in nine of 10 states prioritized for ART scale-up. Weekly program data (October 2019–March 2020) were tracked and analyzed.Results: Of the total 774 LGAs in Nigeria, using SAE, 103 (13.3%) high-burden LGAs were identified, in which 2605 (28.0%) out of 9,294 hotspots were prioritized by mapping newly identified PLHIV by residential addresses. Over 22 weeks, among 882,449 individuals screened using HRST, 723,993 (82.0%) were eligible and tested for HIV (state range, 43.7– 90.4%), out of which 20,616 were positive. Through IT, an additional 3,724 PLHIV were identified. In total, 24,340 PLHIV were identified and 97.4% were linked to life-saving antiretroviral therapy. The number of newly identified PLHIV increased 17-fold over 22 weeks (week 1: 89; week 22: 1,632). Overall mean HIV positivity rate by state was 3.3% (range, 1.8– 6.4%).Conclusion: Using ECCP in nine states in Nigeria increased the number of PLHIV in the community who knew their status, allowing them to access life-saving care and decreasing the risk of HIV transmission.Keywords: ART Surge, small area estimation, HIV risk assessment tool, index partner testing

The hierarchical Bayes predictor of small area proportions (HBP) under an area level version of generalized linear mixed model with logit link function is widely used in small area estimation for b...

Objective:High salt intake is one of the leading diet-related risk factors for several non-communicable diseases. We aimed to estimate the prevalence of high salt intake in Iran.Design:A modelling study by the small area estimation method, based on a nationwide cross-sectional survey, Iran STEPwise approach to risk factor Surveillance (STEPS) 2016. The modelling estimated the prevalence of high salt intake, defined as a daily salt intake ≥ 5 g in all districts of Iran based on data from available districts. The modelling results were provided in different geographical and socio-economic scales to make the comparison possible across the country.Setting:429 districts of all provinces of Iran, 2016.Participants:18 635 salt intake measurements from individuals 25 years old and above who participated in the Iran STEPS 2016 survey.Results:All districts in Iran had a high prevalence of high salt intake. The estimated prevalence of high salt intake among females of all districts ranged between 72·68 % (95 % UI 58·48, 84·81) and 95·04 % (95 % UI 87·10, 100). Estimated prevalence for males ranged between 88·44 % (95 % UI 80·29, 96·15) and 98·64 % (95 % UI 94·97, 100). In all categorisations, males had a significantly higher prevalence of high salt intake. Among females, the population with the lower economic status had a higher salt consumption than the participants with higher economic status by investigating the concentration index.Conclusions:Findings of this study highlight the high salt intake as a prominent risk factor in all Iran regions, despite some variations in different scales. More suitable population-wide policies are warranted to handle this public health issue in Iran.

Over the past decade, statisticians have developed methods to improve generalizations from nonrandom samples using propensity score methods. While these methods contribute to generalization researc...

This paper proposes to investigate inequality in Viet Nam from the point of view of a study of the urban/rural gap by means of a multilevel model. Using data from the Viet Nam Household Living Standards Survey of 2002, the paper constructs a multilevel model, yielding random effects in the urban/rural gap which can be seen as location-specific random contributions to the urban/rural gap above and beyond the effects of known location characteristics, such as the level of education of the population, etc. The paper also demonstrates how the multilevel model can be used to obtain small area estimates at the commune level.

The purpose of the Dutch Travel Survey is to produce reliable estimates on mobility of the Dutch population. In this paper mobility trends are estimated at several aggregation levels, using multilevel time series models. The models account for discontinuities induced by two survey redesigns and outliers due to less reliable outcomes in one particular year. The input for the model is direct annual estimates with their standard errors for the period 1999–2017 for a detailed cross-classification in 504 domains. Appropriate transformations for the direct estimates and generalized variance functions to smooth the standard errors of the direct estimates are proposed. The models are fitted in an hierarchical Bayesian framework using MCMC simulations. From the model outputs smooth trend estimates are computed at the most detailed domain level. Predictions at higher aggregation levels obtained by aggregation of the most detailed domain predictions result in a numerically consistent set of trend estimates for all target variables.

Indonesia is one of many countries around the world that attempt to suffer from high poverty rates. Since, poverty information in a certain area is a point of interest to researchers and policy makers. One problem faced is for the development program to be carried out more effectively and efficiently, it is necessary to have data availability up to the micro-scale. The technique used to reach the goal is Small Area Estimation (SAE). Fay-herriot (FH) model is one method on Small Area Estimation. Since, the SAE techniques require “borrow strength” across neighbor areas so thus Fay-Herriot model approach was developed by integrating spatial information into the model. This method known as Spatial Fay-Herriot Model (SFH) or Spatial Empirical Best Linear Unbiased Prediction (SEBLUP). This study aims to compare MSE of direct estimation, FH, and SFH Model to see which method gives the best result in estimating expenditure. The MSE value of the estimated SFH is smaller than direct estimation and FH, but it does not significant. It means adding spatial information in the small area estimation model does not give a better prediction than the simple small area estimation which is takes account the area as a specific random effect.

The increasing inequality of private income and wealth requires the redistribution of financial resources. Thus, several financial support schemes allocate budget across countries or regions. This work shows how to estimate private wealth at low regional levels by means of a modified Fay-Herriot approach that deals with (a) unit and item non-response, especially with used multiple imputation, (b) the skewness of the wealth distribution, and (c) inconsistencies of the regional estimates with the national direct estimate. One compelling example for financial redistribution is the promoted catching-up process of East Germany after the German reunification. This work shows that 25 years after the reunification differences are more diverse than just between the East and the West by estimating private wealth at two regional levels in Germany. The analysis is based on the Household Finance and Consumption Survey (HFCS) that the European Central Bank launched for all euro area countries in 2010. Although the application in this paper focuses particularly on Germany, the approach proposed is applicable to the other countries participating in the HFCS as well as to other surveys that make use of multiple imputation.

Labor figures for Mexico’s municipalities were estimated during 2018’s first quarter by using Small Area Estimation (SAE) techniques with the incorporation of a spatial component – given there is no recent information source with such a level of geographic disaggregation. To achieve this, combined information from different sources was used to build statistical models in which the Economically Active Population, the Employed Population and the Informal Employed Population were taken as variables object of estimation – this information was taken from the National Survey of Occupation and Employment (ENOE for its acronym in Spanish). Auxiliary variables were selected from population censuses, administrative records, and population projections. The results were contrasted with those calculated by applying the percentage structures of 2010 Population and Housing Census to the figures provided by ENOE at a federal entity level, and with the data in this survey (obtained by direct estimation for those municipalities which had a sufficient sample with acceptable coefficients of variation). It is observed that the results obtained by Small Area Estimation are plausible and register coefficients of variation below 10 percent.

Obesity is considered to be one of the primary health risks in modern industrialized societies. Estimating the evolution of its prevalence over time is an essential element of public health reporting. This requires the application of suitable statistical methods on epidemiologic data with substantial local detail. Generalized linear-mixed models with medical treatment records as covariates mark a powerful combination for this purpose. However, the task is methodologically challenging. Disease frequencies are subject to both regional and temporal heterogeneity. Medical treatment records often show strong internal correlation due to diagnosis-related grouping. This frequently causes excessive variance in model parameter estimation due to rank-deficiency problems. Further, generalized linear-mixed models are often estimated via approximate inference methods as their likelihood functions do not have closed forms. These problems combined lead to unacceptable uncertainty in prevalence estimates over time. We propose an l2-penalized temporal logit-mixed model to solve these issues. We derive empirical best predictors and present a parametric bootstrap to estimate their mean-squared errors. A novel penalized maximum approximate likelihood algorithm for model parameter estimation is stated. With this new methodology, the regional obesity prevalence in Germany from 2009 to 2012 is estimated. We find that the national prevalence ranges between 15 and 16%, with significant regional clustering in eastern Germany.

Changes in the design of a repeated survey generally result in systematic effects in the sample estimates, which are further referred to as discontinuities. To avoid confounding real period-to-period change with the effects of a redesign, discontinuities are often quantified by conducting the old and the new design in parallel for some period of time. Sample sizes of such parallel runs are generally too small to apply direct estimators for domain discontinuities. A bivariate hierarchical Bayesian Fay-Herriot (FH) model is proposed to obtain more precise predictions for domain discontinuities and is applied to a redesign of the Dutch Crime Victimization Survey. This method is compared with a univariate FH model where the direct estimates under the regular approach are used as covariates in a FH model for the alternative approach conducted on a reduced sample size and a univariate FH model where the direct estimates for the discontinuities are modeled directly. An adjusted step forward selection procedure is proposed that minimizes the WAIC until the reduction of the WAIC is smaller than the standard error of this criteria. With this approach more parsimonious models are selected, which prevents selecting complex models that tend to overfit the data.

Changes in the design of a repeated survey generally result in systematic effects in the sample estimates, which are further referred to as discontinuities. To avoid confounding real period-to-period change with the effects of a redesign, discontinuities are often quantified by conducting the old and the new design in parallel for some period of time. Sample sizes of such parallel runs are generally too small to apply direct estimators for domain discontinuities. A bivariate hierarchical Bayesian Fay-Herriot (FH) model is proposed to obtain more precise predictions for domain discontinuities and is applied to a redesign of the Dutch Crime Victimization Survey. This method is compared with a univariate FH model where the direct estimates under the regular approach are used as covariates in a FH model for the alternative approach conducted on a reduced sample size and a univariate FH model where the direct estimates for the discontinuities are modeled directly. An adjusted step forward selection procedure is proposed that minimizes the WAIC until the reduction of the WAIC is smaller than the standard error of this criteria. With this approach more parsimonious models are selected, which prevents selecting complex models that tend to overfit the data.

The EU Statistics on Income and Living Conditions (EU-SILC) has provided annual estimates of the number of labour market indicators for EU countries since 2003, with an almost exclusive focus on national rates. However, it is impossible to obtain reliable direct estimates of labour market statistics at low levels based on the EU-SILC survey. In such cases, model-based small area estimation can be used. In this paper, the low work intensity indicator for the spatial domains in Poland between 2005-2012 was estimated. The Rao and You (1994), Fay and Diallo (2012), and Marhuenda, Molina and Morales (2013) models were applied. The bootstrap MSE for the discussed methods was proposed. The results indicate that these models provide more reliable estimates than direct estimation.

The Fay–Herriot (FH) model is widely used in small area estimation (SAE) for aggregated level data, but in several applications presence of spatial effect between contiguous or neighboring region c...

This paper presents a methodological update to the World Bank's toolkit for small area estimation. The paper reviews the computational procedures of the current methods used by the institution: the traditional ELL approach and the Empirical Best (EB) addition introduced to imitate the original EB procedure of Molina and Rao [Small area estimation of poverty indicators. Canadian J Stat. 2010;38(3):369–385], including heteroskedasticity and survey weights, but using a different bootstrap approach, here referred to as clustered bootstrap. Simulation experiments provide empirical evidence of the shortcomings of the clustered bootstrap approach, which yields biased and noisier point estimates. The document presents an update to the World Bank’s EB implementation by considering the original EB procedures for point and noise estimation, extended for complex designs and heteroscedasticity. Simulation experiments illustrate that the revised methods yield considerably less biased and more efficient estimators than those obtained from the clustered bootstrap approach.

Nowadays, estimation demand in statistics is increased worldwide to seek out an estimate, or approximation, which may be a value which will be used for various purpose, albeit the input data could also be incomplete, uncertain, or unstable. The development of different estimation methods is trying to provide most accurate estimate and estimation theory deals with finding estimates with good properties. The demand of small area estimation (SAE) method has been increasing rapidly around the world because of its reliability compared to the traditional direct estimation methods, especially in the case of small sample size. This paper mainly focuses on the comparison of several indirect small area estimation methods (poststratified synthetic, SSD and EB estimates) with traditional direct estimator based on a renowned data set. Direct estimator is approximately unbiased but SSD and Post-stratified synthetic estimator is extreme biased. To cope up the problem, we conduct another model-based estimation procedure namely Empirical Bayes (EB) estimator, which is unbiased and compare them using their coefficient of variation (CV). To check the model assumption, we used Q-Q plot as well as a Histogram to confirm the normality, bivariate correlation, Akaike information criterion (AIC). JEL classification numbers: C13, C51, C51. Keywords: Small Area Estimation, Direct Estimation, Indirect Estimation, Empirical Bayes Estimator, Poverty Mapping.

In the last few years, diabetes mellitus and obesity revealed to be one of the fastest-growing chronic diseases in youth in the United States. The number of new diabetes cases is dramatically increasing, and, for the moment, effective therapy does not exist. Experts believe that one of the causes of this increase is the decline in exercise behavior. The California Education Code requires local educational agencies (LEAs) to administer the FITNESSGRAM, the Physical Fitness Test (PFT), to Californian students of public schools. This test evaluates six fitness areas, and experts defined that a passing result on all six areas of the test represents a fitness level that offers some protection against the diseases associated with physical inactivity. We consider 2015-2016 data provided by the California Department of Education (CDE): for each Californian county ( m=57 ), we aim at estimating the county-level proportion of students with a score equal to six. To account for the heterogeneity of the phenomenon and the presence of outlying counties, we extend the standard area-level model by specifying the random effects as a symmetric α -stable (S α S) distribution that can accommodate different types of outlying observations. The model can accurately estimate the county-level proportion of students with a score equal to six. Results highlight some interesting relationships with social and economic situations in each county. The performance of the proposed model is also investigated through an extensive simulation study.

The assessment of prevalence on regional levels is an important element of public health reporting. Since regional prevalence is rarely collected in registers, corresponding figures are often estimated via small area estimation using suitable health data. However, such data are frequently subject to uncertainty as values have been estimated from surveys. In that case, the method for prevalence estimation must explicitly account for data uncertainty to allow for reliable results. This can be achieved via measurement error models that introduce distribution assumptions on the noisy data. However, these methods usually require target and explanatory variable errors to be independent. This does not hold when data for both have been estimated from the same survey, which is sometimes the case in official statistics. If not accounted for, prevalence estimates can be severely biased. We propose a new measurement error model for regional prevalence estimation that is suitable for settings where target and explanatory variable errors are dependent. We derive empirical best predictors and demonstrate mean-squared error estimation. A maximum likelihood approach for model parameter estimation is presented. Simulation experiments are conducted to prove the effectiveness of the method. An application to regional hypertension prevalence estimation in Germany is provided.

Background: In 2018, the US Preventive Services Task Force (USPSTF) recommended prostate cancer screening for men aged 55 to 69 years who express a preference for being screened after being informed about and understanding prostate-specific antigen (PSA) test benefits and risks. USPSTF recommended against screening men aged ≥70 years. We aim to generate county-level prevalence estimates, masked by national and state estimates, to identify counties with high PSA screening prevalence. Methods: We fitted multilevel logistic regression mixed models for 4 age groups (≥40, 40 to 54, 55 to 69, ≥70 years), using data from the 2018 Behavioral Risk Factor Surveillance System (BRFSS) (n = 116,654) and other sources. We evaluated consistency between our model-based state and BRFSS direct state estimates with Spearman and Pearson correlation coefficients. Results: PSA screening prevalence increased with increasing age groups: 7.7% for men aged 40 to 54 years, 27.2% for men aged 55 to 69 years, and 33.7% among men age ≥70 years, and was largely clustered in the South and Appalachia. Many county estimates among men aged ≥70 years exceeded 40%, especially in the South. Correlation coefficients were 0.94 for men aged ≥40, and ≥0.85 for men aged 40 to 54 years, 55 to 69 years, and ≥70 years. Conclusions: PSA screening was highest among men ≥70 years, for whom it is not recommended, and in the South among all age groups. Screening varied substantially within states. Impact: In 2018, on average, more than 1 in 4 men aged 55 to 69 years and 1 in 3 men aged ≥70 years underwent PSA screening in the prior year, suggesting potential overuse among some men.

Per capita expenditure of an area is a welfare indicator of the community. It is also a reflection of the economic capacity in meeting basic needs. Bali is the second richest province in Indonesia. This study aims to model the per capita expenditure of Bali at the sub-district level using Spatial-EBLUP (SEBLUP) approach in SAE. Small area estimation (SAE) modeling is an indirect estimation approach capable of increasing the effectiveness of sample sizes and minimizing variance. The heterogeneity of an area is influenced by other areas around. Everything is related to one another, but something closer will be more influential than something far away. Therefore, the spatial effect can be included in the random effect of a model small area, which is called as SEBLUP model. The selection of a spatial weights matrix is very important in spatial data modeling. It represents the neighborhood relationship of each spatial observation unit. A SEBLUP model needs a spatial weights matrix, which can be based on distance (radial distance and power distance), contiguity (queen), and a combination of distance and contiguity (radial distance and queen contiguity). The result of the implementation of the SEBLUP approach in per capita expenditure of Bali shows that the SEBLUP model with radial distance spatial weights matrix is the best model with the smallest ARMSE. South Denpasar Sub-district is the most prosperous sub-district with the highest per capita expenditure in Bali. Meanwhile, Abang Sub-district is the smallest per capita expenditure.