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Key message: A nonlinear mixed effects canopy density model developed with predictor variables describing stand characteristics and soil nutrients provides a high prediction accuracy. Canopy density (CD) of a forest stand is an indicator of describing tree vitality, tree growth, competition status, environmental condition, and climate change. CD is substantially influenced by several site and environmental factors, such as soil, terrain, and stand factors. However, the CD prediction model developed utilizing the important site and environmental factors is still lacking. This study developed a nonlinear mixed-effects (NLME) CD model using data from 259 sample plots distributed across the moso bamboo (Phyllostachys edulis) forests in the eight provinces of southern China. Like fast-growing tree species, moso bamboo has high rates of growth and carbon sequestration, accumulating large amount of biomass in a short period. The CD model includes the effects of factors describing characteristics of terrains, soil and forest stands. The results showed that elevation significantly affected CD. The NLME CD model developed with the significant predictors included are: stand density (N), dominant height (DH), base area (BA), total nitrogen (TN), and soil organic carbon (SOC). When modeling random effects at the provincial level, the fitting accuracy of the model was significantly improved. Among several strategies used in calibrating NLME CD model or estimating random effects, an increased accuracy was obtained with increasing number of sample plots. However, using many sample plots per province to calibrate NLME CD model may increase the inventory costs with a little gain in the accuracy. Using the two medium BA-plots in each province, slope, and elevation or two largest BA-plots at the different slope-aspect could provide a compromise between measurement cost, model use efficiency, and prediction accuracy. NLME CD model can reduce measurement requirements in the field and support forest managers for more effective bamboo forest management strategies. [ABSTRACT FROM AUTHOR]

Along with the growing popularity of the small area estimation method, the need to utilize good auxiliary variables also increases. Remote sensing data, such as night light imagery, offers advantages such as time-cost efficiency and global coverage but is easily accessible. This research aims to implement night light intensity as an auxiliary variable for the EBLUP model to estimate per capita consumption expenditure at West Java in 2018. This research employs three scenarios of auxiliary variables usage in EBLUP model construction: official data, night light intensity, and the combination between both data. The results show that night light intensity is an efficient auxiliary variable for estimating per capita consumption expenditure. Furthermore, the EBLUP model with a combination of official data and night light as auxiliary variables gives the best accuracy with coefficient of variation (CV) as evaluation. [ABSTRACT FROM AUTHOR]

The known connection between shrinkage estimation, empirical Bayes, and mixed effects models is explored and applied to balanced and unbalanced designs in which the responses are correlated. As an illustration, a mixed model is proposed for predicting the outcome of English Premier League games that takes into account both home and away team effects. Results based on empirical best linear unbiased predictors obtained from fitting mixed linear models are compared with fully Bayesian predictors that utilize prior information from the previous season. [ABSTRACT FROM AUTHOR]

Crop statistics for a small area, such as the community development block, are an increasingly important topic in agricultural statistics. Under normality assumptions, the classic Empirical Best Linear Unbiased Prediction (EBLUP) technique is effective for predicting small area means, however the Small Area Estimation (SAE) model can be heavily affected by the incidence of outliers or deviations from the expected distribution. The purpose of this study was to estimate variance, predict block-level wheat crop yield in the Hisar and Sirsa district of Haryana by classical SAE method and a robust random-effect predictor using a slight generalization of Huber's Proposal 2. In the case of Sirsa district, the results of classical and robust unit level SAE were very close, but not in the case of Hisar district. This could be due to the influential observation found in the Hisar data set. More accurate EBLUP wheat yield estimates are obtained when the Huber-type M-estimation method is initialized by the least square regression estimator. [ABSTRACT FROM AUTHOR]

Background: Because micronutrient deficiencies affect public health, countries monitor population status by national-scale, multi-stage, micronutrient surveys (MNS). In design-based surveys, inclusion probabilities are specified for sample units and the corresponding sample weights allow design-unbiased estimates to be made of population parameters. Corrections may be possible on departures from the design; an alternative is to use linear mixed models (LMM), with an estimated covariance structure reflecting the sampling design, to obtain model-based estimates., Design: The Ethiopia National Micronutrient Survey (2016) specified inclusion probabilities at enumeration area (EA) and household (HH) levels, and sample weights are provided. However, the design was not followed as it would have resulted in insufficient sampling from women of reproductive age., Results: Having found no evidence that sample weights were informative for target serum micronutrient concentrations (Zn), we estimated LMM parameters, with Regions as fixed effects, and the variation of individuals nested within households, households within EA, and EA within regions, random effects. We obtained LMM standard errors, Best Linear Unbiased Estimates (BLUEs) of regional means, and empirical Best Linear Unbiased Predictions for sampled/unsampled EA and HH. The probability that each true regional mean exceeded the sufficiency threshold ( 65 μ g dL - 1 ) was evaluated. The variances of BLUEs of regional means, under alternative sampling designs, were bootstrapped from LMM variance components., Conclusions: We demonstrate use of LMM to obtain model-unbiased estimates and predictions when surveys deviate from the original design; and the use of LMM variance components to evaluate alternative designs for further sampling, or for sampling comparable populations., Competing Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2024.)

One of the data needed is per capita expenditure of sub-district level. The National Socio-Economic Survey (Susenas) obtain per capita expenditure data. However, due to limited samples, Susenas cannot get statistical information down to the sub-district or village level from this survey. Therefore, a model that includes additional data (census data) to estimate sub-district levels uses Small Area Estimation (SAE) modelling. In this study, the Empirical Best Linear Unbiased Prediction (EBLUP) method estimates the per capita expenditure of sub-district levels in Jambi Province in 2018. The EBLUP modelling also applies cluster information to estimate per capita expenditure in the sub-districts that are not surveyed (non-sampled area). The K-Medoids Cluster method is used to get sub-district clusters based on their characteristics. The mean of area random effects per cluster adds to the prediction model for the non-sampled area. This study aims to compare and evaluate the direct estimation method and EBLUP method to estimate sub-district level per capita expenditure based on Relative Root Mean Square Error (RRMSE). The result shows that EBLUP estimation produces more accurate estimates than direct estimation. This research also estimates the per capita expenditure of non-sampled areas using the EBLUP method by applying K-Medoids Cluster information. [ABSTRACT FROM AUTHOR]

This paper demonstrates a process for translating a database of forest measurements to interactive dashboards through which users can access statistically defensible estimates and analyses anywhere in the conterminous US. It taps the extensive Forest Inventory and Analysis (FIA) plot network along with national remotely sensed data layers to produce estimates using widely accepted model-assisted and small area estimation methodologies. It leverages a decade’s worth of statistical and computational research on FIA’s flexible estimation engine, FIESTA, and provides a vehicle through which scientists and analysts can share their own tools and analytical processes. This project illustrates one pathway to moving statistical research into operational inventory processes, and makes many model-assisted and small area estimators accessible to the FIA community. To demonstrate the process, continental United States (CONUS)-wide model-assisted and small area estimates are produced for ecosubsections, counties, and level 5 watersheds (HUC 10) and made publicly available through R Shiny dashboards. Target parameters include biomass, basal area, board foot volume, proportion of forest land, cubic foot volume, and live trees per acre. Estimators demonstrated here include: the simplest direct estimator (Horvitz–Thompson), model-assisted estimators (post-stratified, generalized regression estimator, and modified generalized regression estimators), and small area estimators (empirical best linear unbiased predictors and hierarchical Bayes both at the area- and unit-level). Auxiliary data considered in the model-assisted and small area estimators included maps of tree canopy, tree classification, and climatic variables. Estimates for small domain sets were generated nationally within a few hours. Exploring results across estimators and target variables revealed the progressive gains in precision using (in order of least gain to highest gain) Horvitz–Thompson, post-stratification, modified generalized regression estimators, generalized regression estimators, area-level small area models, and unit-level small area models. Substantive gains are realized by expanding model-assisted estimators beyond post-stratification, allowing FIA to continue to take advantage of design-based inference in many cases. Caution is warranted in the use of unit-level small area models due to model mis-specification. The dataset of estimates available through the dashboards provides the opportunity for others to compare estimators and explore precision expectations over specific domains and geographic regions. The dashboards also provide a forum for future development and analyses.

Small area estimation (SAE) plays a crucial role in the social sciences due to the growing need for reliable and accurate estimates for small domains. In the study of well-being, for example, policy makers need detailed information about the geographical distribution of a range of social indicators. We investigate data dimensionality reduction using factor analysis models and implement SAE on the factor scores under the empirical best linear unbiased prediction approach. We contrast this approach with the standard approach of providing a dashboard of indicators or a weighted average of indicators at the local level. We demonstrate the approach in a simulation study and a real data application based on the European Union Statistics for Income and Living Conditions for the municipalities of Tuscany. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation. [ABSTRACT FROM AUTHOR]

Worry about crime is known to be higher in some European regions than others. However, cross-national surveys, which are the main source of information to map worry about crime across Europe, are designed to be representative of large areas (countries), and regions often suffer from small and unrepresentative sample sizes. This research produces reliable model-based small area estimates of worry about crime at regional level from European Social Survey data, in order to map the phenomenon and examine its macro-level predictors. Model-based small area estimation techniques borrow strength across areas to produce reliable estimates of parameters of interest. Estimates of worry about crime are higher in most South and East European regions, in contrast to Northern and Central Europe. [ABSTRACT FROM AUTHOR]

Multivariate Fay-Herriot (MFH) models become popular methods to produce reliable parameter estimates of some related multiple characteristics of interest that are commonly produced from many surveys. This article studies the application of MFH models for estimating household consumption per capita expenditure (HCPE) on food and HCPE of non-food. Both of those associated direct estimates, which are obtained from the National Socioeconomic Surveys conducted regularly by Statistics Indonesia, have a strong correlation. The effects of correlation in MFH models are evaluated by employing a simulation study. The simulation showed that the strength of correlation between variables of interest, instead of the number of domains, plays a prominent role in MFH models. The application showed that MFH models have more efficient than univariate models in terms of standard errors of regression parameter estimates. The roots of mean squared errors (RMSEs) of the estimates obtained from the empirical best linear unbiased prediction (EBLUP) estimators of MFH models are smaller than RMSEs obtained from the direct estimators. Based on MFH model, the HCPE estimates of food by districts in Central Java, Indonesia, are higher than the HCPE estimates of non-food. The average of HCPE estimates of food and non-food in Central Java, Indonesia in 2015 are IDR 383,100.6 and IDR 280,653.6, respectively. [ABSTRACT FROM AUTHOR]

Spatial data contains of observation and region information, can describes spatial patterns such as social phenomenon or poverty. In poverty parameter estimations, the less of sample adequacy to deliver direct estimation is one of the limitation, thus the Small Area Estimation (SAE) developed to handle it. Since, the small area estimation techniques require “borrow strength” across the neighbor areas furthermore SAE was developed by integrating spatial information into the model, named as Spatial SAE. Therefore, the purpose of this paper is to compare the SAE and Spatial SAE model in order to estimate, at sub-district level, mean per capita income of each area using the poverty survey data in Bangka Belitung province at 2017 by Polytechnic of Statistics STIS. The findings of the paper is spatial information don’t influence the parameter estimation in SAE. [ABSTRACT FROM AUTHOR]

Accurate estimates of growth and structural changes are key for forest management tasks such as determination of optimal rotation times, optimal rotation times, site indices and for identifying areas experiencing difficulties to regenerate. Estimation of structural changes, especially for biomass, is also key to quantify greenhouse gas (GHG) emissions/sequestration. We compared two different modeling strategies to estimate changes in V, BA and B, at three different spatial aggregation levels using auxiliary information from two light detection and ranging (LiDAR) flights. The study area is Blacks Mountains Experimental Forest, a ponderosa pine dominated forest in Northern California for which two LiDAR acquisitions separated by six years were available. Analyzed strategies consisted of (1) directly modeling the observed changes as a function of the LiDAR auxiliary information ( δ -modeling method) and (2) modeling V, BA and B at two different points in time, including a term to account for the temporal correlation, and then computing the changes as the difference between the predicted values of V, BA and B for time two and time one. We analyzed predictions and measures of uncertainty at three different level of aggregation (i.e., pixels, stands or compartments and the entire study area). Results showed that changes were very weakly correlated with the LiDAR auxiliary information. Both modeling alternatives provided similar results with a better performance of the δ -modeling for the entire study area; however, this method also showed some inconsistencies and seemed to be very prone to extrapolation problems. The y -modeling method, which seems to be less prone to extrapolation problems, allows obtaining more outputs that are flexible and can outperform the δ -modeling method at the stand level. The weak correlation between changes in structural attributes and LiDAR auxiliary information indicates that pixel-level maps have very large uncertainties and estimation of change clearly requires some degree of spatial aggregation; additionally, in similar environments, it might be necessary to increase the time lapse between LiDAR acquisitions to obtain reliable estimates of change.

Many target variables in official statistics follow a semicontinuous distribution with a mixture of zeros and continuously distributed positive values. Such variables are called zero inflated. When reliable estimates for subpopulations with small sample sizes are required, model-based small-area estimators can be used, which improve the accuracy of the estimates by borrowing information from other subpopulations. In this article, three small-area estimators are investigated. The first estimator is the EBLUP, which can be considered the most common small-area estimator and is based on a linear mixed model that assumes normal distributions. Therefore, the EBLUP is model misspecified in the case of zero-inflated variables. The other two small-area estimators are based on a model that takes zero inflation explicitly into account. Both the Bayesian and the frequentist approach are considered. These small-area estimators are compared with each other and with design-based estimation in a simulation study with zero-inflated target variables. Both a simulation with artificial data and a simulation with real data from the Dutch Household Budget Survey are carried out. It is found that the small-area estimators improve the accuracy compared to the design-based estimator. The amount of improvement strongly depends on the properties of the population and the subpopulations of interest. [ABSTRACT FROM AUTHOR]

Empirical best linear unbiased predictors (EBLUPs) based on auxiliary information are efficient for estimating means or totals of environmental attributes in small domains. In small area estimation, the EBLUPs and their approximately unbiased mean square error (MSE) estimators are obtained under the premise of having a large number of population units in the target domain. In remote sensing, single pixels are regarded as population units, and EBLUPs and MSE estimators may also be required for subdomains containing a low number of pixels or even single pixels. In this study, EBLUPs, their MSE, and an unbiased estimator of the MSE are derived when predicting linear parameters for subdomains with a small number of population units that do not intersect with the training sample. In these situations, an additional MSE component should be considered to prevent MSE underestimation. A case study illustrates the applicability of the obtained results in the context of a Light Detection and Ranging-based forest inventory, where estimates are provided for areas of interest sizing from single pixels or population units to thousands of hectares. Based on our results, we recommend to consider the additional component in the MSE estimator when estimating in pixels and domains of interest sizing few hectares. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Liveability is a concept closely related to the notion of well-being and refers to the environmental conditions that contribute to the quality of life, alongside individual features. Subjective and objective measurements of liveability are both of considerable practical and theoretical importance. A survey is conducted in this paper by which individuals tend to shape their preferences according to six factors describing various aspects of living conditions: (1) home, (2) neighbourhood, (3) transport, (4) entertainment, (5) services and (6) work. The survey data helps us to work out some indicators representing the perceived liveability in the targeted areas. A linear mixed model is used to explore possible relationships between objective factors and perceived liveability. A model-based estimate of liveability index can be then calculated for each non-sampled individual based on his/her socio-demographic characteristics and area of living. [ABSTRACT FROM AUTHOR]

If unit-level data are available, small area estimation (SAE) is usually based on models formulated at the unit level, but they are ultimately used to produce estimates at the area level and thus involve area-level inferences. This paper investigates the circumstances under which using an area-level model may be more effective. Linear mixed models (LMMs) fitted using different levels of data are applied in SAE to calculate synthetic estimators and empirical best linear unbiased predictors (EBLUPs). The performance of area-level models is compared with unit-level models when both individual and aggregate data are available. A key factor is whether there are substantial contextual effects. Ignoring these effects in unit-level working models can cause biased estimates of regression parameters. The contextual effects can be automatically accounted for in the area-level models. Using synthetic and EBLUP techniques, small area estimates based on different levels of LMMs are investigated in this paper by means of a simulation study. [ABSTRACT FROM AUTHOR]

Small area estimates based on the widely used area-level model proposed in Fay and Herriot (1979) assume that the area-level direct estimates are spatially uncorrelated. In many cases, however, this is not the case. Extensions of the Fay-Herriot model to allow for spatial correlation have been proposed, but all assume spatial stationarity; i.e., the parameters of the associated regression model for the small area characteristic of interest do not vary spatially. Instead, spatial effects are introduced by imposing a spatial correlation structure on the regression errors. In this paper, we propose an extension to the Fay-Herriot model that accounts for the presence of spatial nonstationarity, i.e., where the parameters of this regression model vary spatially. We refer to the predictor based on this extended model as the nonstationary empirical best linear unbiased predictor (NSEBLUP). We also develop two different estimators for the mean squared error of the NSEBLUP. The first estimator uses approximations similar to those in Opsomer, Claeskens, Ranalli, Kauermann, and Breidt (2008). The second estimator is based on the parametric bootstrapping approach of Gonzalez-Manteiga, Lombardia, Molina, Morales, and Santamaria (2008) and Molina, Salvati, and Pratesi (2009). Results from model-based and design-based simulation studies using spatially nonstationary data indicate that the NSEBLUP compares favorably with alternative area-level predictors that ignore this spatial nonstationarity. In addition, both proposed methods for estimating its mean squared error seem adequate. [ABSTRACT FROM AUTHOR]

In a special case of the general linear mixed model, one random component obeys a spatial autoregressive process and another a temporal autoregressive process. The population and any affiliations to subpopulations may change in time. The empirical best linear unbiased predictor is derived and may be used even if the sample size in the subpopulation is null in the period of interest. The mean squared error and its estimator are expressed. The accuracy of the predictor and the bias of the mean squared error estimator are addressed through simulations. [ABSTRACT FROM AUTHOR]

Statistical agencies are interested to report precise estimates of linear parameters from small areas. This goal can be achieved by using model-based inference. In this sense, random regression coefficient models provide a flexible way of modelling the relationship between the target and the auxiliary variables. Because of this, empirical best linear unbiased predictor (EBLUP) estimates based on these models are introduced. A closed-formula procedure to estimate the mean-squared error of the EBLUP estimators is also given and empirically studied. Results of several simulation studies are reported as well as an application to the estimation of household normalized net annual incomes in the Spanish Living Conditions Survey. [ABSTRACT FROM AUTHOR]

A nested-error regression model having both fixed and random effects is introduced to estimate linear parameters of small areas. The model is applicable to data having a proportion of domains where the variable of interest cannot be described by a standard linear mixed model. Algorithms and formulas to fit the model, to calculate EBLUP and to estimate mean-squared errors are given. A Monte Carlo simulation experiment is presented to illustrate the gain of precision obtained by using the proposed model and to obtain some practical conclusions. A motivating application to Spanish Labour Force Survey data is also given. [ABSTRACT FROM AUTHOR]

We show that the maximum likelihood estimators (MLEs) of the fixed effects and within-cluster correlation are consistent in a heteroscedastic nested-error regression (HNER) model with completely unknown within-cluster variances under mild conditions. The result implies that the empirical best linear unbiased prediction (EBLUP) method for small area estimation is valid in such a case. We also show that ignoring the heteroscedasticity can lead to inconsistent estimation of the within-cluster correlation and inferior predictive performance. A jackknife measure of uncertainty for the EBLUP is developed under the HNER model. Simulation studies are carried out to investigate the finite-sample performance of the EBLUP and MLE under the HNER model, with comparisons to those under the nested-error regression model in various situations, as well as that of the jackknife measure of uncertainty. The well-known Iowa crops data is used for illustration. The Canadian Journal of Statistics 40: 588-603; 2012 © 2012 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

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The need for small area estimates is increasingly felt in both the public and private sectors in order to formulate their strategic plans. It is now widely recognized that direct small area survey estimates are highly unreliable owing to large standard errors and coefficients of variation. The reason behind this is that a survey is usually designed to achieve a specified level of accuracy at a higher level of geography than that of small areas. Lack of additional resources makes it almost imperative to use the same data to produce small area estimates. For example, if a survey is designed to estimate per capita income for a state, the same survey data need to be used to produce similar estimates for counties, subcounties and census divisions within that state. Thus, by necessity, small area estimation needs explicit, or at least implicit, use of models to link these areas. Improved small area estimates are found by "borrowing strength" from similar neighboring areas. The key to small area estimation is shrinkage of direct estimates toward some regression estimates obtained by using in addition administrative records and other available sources of information. These shrinkage estimates can often be motivated from both a Bayesian and a frequentist point of view, and indeed in this particular context, it is possible to obtain at least an operational synthesis between the two paradigms. Thus, on one hand, while small area estimates can be developed using a hierarchical Bayesian or an empirical Bayesian approach, similar estimates are also found using the theory of best linear unbiased prediction (BLUP) or empirical best linear unbiased prediction (EBLUP). The present article discusses primarily normal theory-based small area estimation techniques, and attempts a synthesis between both the Bayesian and the frequentist points of view. The results are mostly discussed for random effects models and their hierarchical Bayesian counterparts. A few miscellaneous remarks are made at the end describing the current research for more complex models including some nonnormal ones. Also provided are some pointers for future research. [ABSTRACT FROM AUTHOR]

In many situations, information on stem diameters inside bark (dib) are more desirable than on diameters outside bark (dob). However, obtaining dib measurements is usually expensive, time-consuming, and prone to significant measurement errors when done on standing trees. Many bark thickness equations have been proposed to estimate the dibs of standing trees. In this study, we compared several commonly used bark thickness equations for seven conifer species in the Acadian Region of North America. Mixed-effects modeling techniques were employed to fit linear and non-linear bark thickness equations. We found the equation proposed by Cao and Pepper (South J Appl Forestry 10:220-224, 1986; Eq. 5) performed significantly better than other equations for most of our study species. The Cao and Pepper (South J Appl Forestry 10:220-224, ) equation is a function of dob, relative height in the stem, tree height, and the ratio of dib to dob at breast height. The mean absolute bias was found to be reduced up to 74% compared with using a fixed ratio approach employed in the widely used Northeastern variant of the Forest Vegetation Simulator (FVS-NE) growth and yield model. Leave-one-out cross validation was further performed to determine the location of suitable prior measurements in the prediction process for three of the most well-behaved equations. Results show that no unified prior measurement can provide best predictive abilities across all species as the choice of prior dib measurements depends on both species and bark thickness equations. [ABSTRACT FROM AUTHOR]

A modification of the Fay-Herriot model is introduced to treat situations where small areas are divided in two groups and domain random effects have different variances across the groups. The model is applicable to data having a large subset of domains where direct estimates of the variable of interest cannot be described in the same way as in its complementary subset of domains. This is generally the case when domains are constructed by crossing geographical characteristics with sex. Algorithms and formulas to fit the model, to calculate EBLUPs and to estimate mean squared errors are given. Monte Carlo simulation experiments are presented to illustrate the gain of precision obtained by using the proposed model and to get some practical conclusions. A motivating application to Spanish Labour Force Survey data is also given. [ABSTRACT FROM AUTHOR]

Abstract: This work aims to predict exponentials of mixed effects under a multivariate linear regression model with one random factor. Such quantities are of particular interest in prediction problems where the dependent variable is the logarithm of the variable that is the object of inference. Bias-corrected empirical predictors of the target quantities are defined. A second-order approximation for the mean crossed product error of two of these predictors is obtained, where the mean squared error is a particular case. An estimator of the mean crossed product error with second-order bias is proposed. Finally, results are illustrated through an application related to small area estimation. [Copyright &y& Elsevier]

Statistics for small areas within larger regions are recently required for many economic variables. However, when adding the estimates of the small areas within the larger regions, the results do not match up to those obtained with the appropriate estimator originally derived for the larger region. To avoid discrepancies between estimates benchmarking methods are commonly used in practice. In this paper, we discuss the suitability of using a restricted predictor versus a traditional direct calibrated estimator. The results are illustrated with the 2000 Business Survey of the Basque Country, Spain. [ABSTRACT FROM AUTHOR]

Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163-171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior than the Prasad-Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors. [ABSTRACT FROM AUTHOR]

Over the last three decades, mixed models have been frequently used in a wide range of small area applications. Such models offer great flexibilities in combining information from various sources, and thus are well suited for solving most small area estimation problems. The present article reviews major research developments in the classical inferential approach for linear and generalized linear mixed models that are relevant to different issues concerning small area estimation and related problems. [ABSTRACT FROM AUTHOR]

A comparison was made of three small-area sampling methods [two traditional design-based methods (ratio-synthetic, sample-size dependent) and one model-based method (EBLUP)] in estimation of some cow and sow population productivity parameters. Performance was evaluated in estimating both farm-specific mean responses and mean animal response over all farms using sample sizes of 100 and 25. Differences in results obtained with the cow and sow data are discussed in terms of the impact of sample size and population size on sampling method. There was a tendency for the model-based method to be the best performer in situations most likely to be operational when the sampling is done as part of a food–animal monitoring scheme. The situations are identified where the sample-size-dependent method performed best. [Copyright &y& Elsevier]

• A mixed-effects height to crown base model (hcb) was developed using LiDAR and field datasets. • LiDAR-derived tree height, crown width and dominant height significantly contributed to the model. • The developed nonlinear mixed effects hcb model showed the best prediction performance. • Five medium trees were found to be the recommended number to estimate the random-effects. Height to crown base (hcb) is an important tree-level characteristic used for determination of crown size and for prediction of the initiation and propagation potential of crown fires. Crown size variables are often used as input variables for forest growth and yield models. In this study, a nonlinear mixed-effects hcb model was developed using measurements from 510 Picea crassifolia Kom trees in 16 sample plots in the Xishui forest farm of SunanYuguzu Autonomous County, Gansu Qilian Mountain National Nature Reserve, China. The modeling data were based on the airborne light detection and ranging (LiDAR), which serves as a reliable database for large forest areas. In general, field-based measurements are considered relatively more accurate compared with remote sensing data, but the LiDAR database can be applied for large forest area at a relatively low inventory cost when appropriate hcb prediction models are available. Given that measurements from the same sample plots were significantly correlated, we incorporated the random-effect component in the model to account for hcb variations at the sample plot-level. Among several potential predictors evaluated, we observed that diameter at breast height, LiDAR-derived total tree height, LiDAR-derived crown width, and LiDAR-derived plot dominant tree height were highly significant in the nonlinear mixed-effects hcb model. Four strategies for selection of sample trees per sample plot (largest trees, medium-sized trees, smallest trees, and randomly selected trees) and seven sample sizes (two to eight selected trees per sample plot) were evaluated for calibration of our nonlinear mixed-effects hcb model. The empirical best linear unbiased prediction method was applied to estimate the random effects for calibration and sample plot-specific hcb prediction. Calibration results revealed increased accuracy with increased number of selected trees per sample plot. However, selecting many sample trees per sample plot to calibrate the nonlinear mixed-effects hcb model may increase inventory costs with little gain in accuracy. Therefore, we recommended, in our study, that selection of five medium-sized trees per sample plot provides a compromise between measurement cost, model use efficiency, and prediction accuracy. [ABSTRACT FROM AUTHOR]

This research examines the geographical distribution of perceived neighbourhood disorder in Manchester, England, by using small area estimates. Sample surveys are the main source of information to analyse perceived disorder. However, most surveys are only representative of large areas, and direct estimates may be unreliable at small area level. Small area estimation techniques borrow strength from related areas to produce reliable small area estimates. This research produces Spatial Empirical Best Linear Unbiased Predictor (SEBLUP) estimates, which account for spatially correlated random area effects, of perceived neighbourhood disorder from the Manchester Resident Telephone Survey. The highest levels of perceived disorder are found in the city centre and some Northern and Central-Eastern areas. Perceived disorder is higher in areas with higher population churn, income deprivation and crime. Small area estimation techniques are a potential tool to map perceived disorder. • Direct estimators produce unreliable estimates at small area level. • The SEBLUP produces the most reliable estimates at small area level. • Disorder is perceived as higher in areas with higher population churn. • Perceived disorder is also higher in economically deprived neighbourhoods. • Perceived disorder is higher in the Manchester city centre and most Northern areas. [ABSTRACT FROM AUTHOR]

Accurate estimates of growth and structural changes are key for forest management tasks such as determination of optimal rotation times, optimal rotation times, site indices and for identifying areas experiencing difficulties to regenerate. Estimation of structural changes, especially for biomass, is also key to quantify greenhouse gas (GHG) emissions/sequestration. We compared two different modeling strategies to estimate changes in V, BA and B, at three different spatial aggregation levels using auxiliary information from two light detection and ranging (LiDAR) flights. The study area is Blacks Mountains Experimental Forest, a ponderosa pine dominated forest in Northern California for which two LiDAR acquisitions separated by six years were available. Analyzed strategies consisted of (1) directly modeling the observed changes as a function of the LiDAR auxiliary information (δ -modeling method) and (2) modeling V, BA and B at two different points in time, including a term to account for the temporal correlation, and then computing the changes as the difference between the predicted values of V, BA and B for time two and time one. We analyzed predictions and measures of uncertainty at three different level of aggregation (i.e., pixels, stands or compartments and the entire study area). Results showed that changes were very weakly correlated with the LiDAR auxiliary information. Both modeling alternatives provided similar results with a better performance of the δ -modeling for the entire study area; however, this method also showed some inconsistencies and seemed to be very prone to extrapolation problems. The y -modeling method, which seems to be less prone to extrapolation problems, allows obtaining more outputs that are flexible and can outperform the δ -modeling method at the stand level. The weak correlation between changes in structural attributes and LiDAR auxiliary information indicates that pixel-level maps have very large uncertainties and estimation of change clearly requires some degree of spatial aggregation; additionally, in similar environments, it might be necessary to increase the time lapse between LiDAR acquisitions to obtain reliable estimates of change. [ABSTRACT FROM AUTHOR]