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In many applications of small area estimation, dichotomous or categorical outcomes are the targets of statistical inference. For example, in the analysis of labour markets, proportions of working-age people in the various labour market statuses are of interest. In this paper, in line with the recent literature, we consider a classification with more than three statuses and estimate related population parameters for 611 local labour market areas using data from the 2012 Italian Labour Force Survey, administrative registers and the 2011 Census. As for the methodology, we propose multinomial expectile regression models. These models provide a means to utilise (Formula presented.) -quantile type approaches, which have been shown to be a useful alternative to mixed model approaches when parametric assumptions on the distribution of random effects cannot be met. Via a large-scale simulation study, we show how this novel approach is much faster and provides reliable results when compared to multinomial mixed model approaches, and works for any number of categories rather than just a small number of categories as is more commonly the case with existing methods. Furthermore, the proposed approach potentially provides a framework for developing other methods for prediction with multi-category outcomes.

Health-related quality of life assessment is important in the clinical evaluation of patients with metastatic disease that may offer useful information in understanding the clinical effectiveness of a treatment. To assess if a set of explicative variables impacts on the health-related quality of life, regression models are routinely adopted. However, the interest of researchers may be focussed on modelling other parts (e.g. quantiles) of this conditional distribution. In this paper, we present an approach based on quantile and M-quantile regression to achieve this goal. We applied the methodologies to a prospective, randomized, multi-centre clinical trial. In order to take into account the hierarchical nature of the data we extended the M-quantile regression model to a three-level random effects specification and estimated it by maximum likelihood

Radon is a natural gas known to be the main contributor to natural background radiation exposure and only second to smoking as major leading cause of lung cancer. The main concern is in indoor environments where the gas tends to accumulate and can reach high concentrations. The primary contributor of this gas into the building is from the soil although architectonic characteristics, such as building materials, can largely affect concentration values. Understanding the factors affecting the concentration in dwellings and workplaces is important both in prevention, when the construction of a new building is being planned, and in mitigation when the amount of Radon detected inside a building is too high. In this paper we investigate how several factors, such as geologic typologies of the soil and a range of building characteristics, impact on indoor concentration focusing, in particular, on how concentration changes as a function of the floor level. Adopting a mixed effects model to account for the hierarchical nature of the data, we also quantify the extent to which such measurable factors manage to explain the variability of indoor radon concentration

One popular approach to small area estimation when data are spatially correlated is to employ Simultaneous Autoregressive (SAR) random effects models to define the Spatial Empirical Best Linear Unbiased Predictor (SEBLUP). See Singh et al. (2005) and Pratesi and Salvati (2008). SAR models allow for spatial correlation in the error structure. An alternative approach that incorporates the spatial information in the regression model is to use Geographically Weighted Regression (GWR). See Brunsdon et al. (1996) and Fotheringham et al. (1997). GWR extends the traditional regression model by characterising the relationship between the outcome variable and the covariates via local rather than global parameters. In this paper we investigate GWR-based small area estimation under the M-quantile modelling approach (Chambers and Tzavidis, 2006). In particular, we integrate the concepts of outlier-robust small area estimation and borrowing strength over space within a unified modelling framework by specifying an M-quantile GWR model that is a local model for the M-quantiles of the conditional distribution of the outcome variable given the covariates. This model is then used to define an outlier-robust predictor of the small area characteristic of interest that also accounts for spatial association in the data. An additional important spin-off from applying the M-quantile GWR small area model is more efficient synthetic estimation for out of sample areas. We demonstrate the usefulness of this framework through both model-based as well as design-based simulation, with the latter based on a realistic survey data set. The paper concludes with an application to environmental data for predicting average levels of the Acid Neutralizing Capacity at 8-digit Hydrologic Unit Code level in the Northeast states of the U.S.A.

In recent years there have been significant developments in model-based small area methods that incorporate spatial information in an attempt to improve the efficiency of small area estimates by borrowing strength over space. A popular approach parametrically models spatial correlation in area effects using Simultaneous Autoregressive (SAR) random effects models. An alternative approach incorporates the spatial information via M-quantile Geographically Weighted Regression (GWR), which fits a local model to the M-quantiles of the conditional distribution of the outcome variable given the covariates. A further approach uses spline approximations to fit nonparametric unit level nested error regression and M-quantile regression models that reflect spatial variation in the data and then uses these nonparametric models for small area estimation. In this presentation we contrast the performance of these alternative small area models using data with geographical information. We also examine how these models perform when estimation is for out of sample areas i.e. areas with zero sample, and discuss issues related to estimation of mean squared error of the resulting small area estimators. Our analysis is illustrated using simulations based on data from the U.S. Environmental Protection Agency’s Environmental Monitoring and Assessment Program.

Small area estimation techniques have typically relied on plug-in estimation based on models containing random area effects. More recently, regression M-quantiles have been suggested for this purpose, thus avoiding conventional Gaussian assumptions, as well as problems associated with the specification of random effects. However, the plug-in M-quantile estimator for the small area mean can be shown to be the expected value of this mean with respect to a generally biased estimator of the small area cumulative distribution function of the characteristic of interest. To correct this problem, we propose a general framework for robust small area estimation, based on representing a small area estimator as a functional of a predictor of this small area cumulative distribution function. Key advantages of this framework are that it naturally leads to integrated estimation of small area means and quantiles and is not restricted to M-quantile models. We also discuss mean squared error estimation for the resulting estimators, and demonstrate the advantages of our approach through model-based and design-based simulations, with the latter using economic data collected in an Australian farm survey.

Outliers are a well-known problem in survey estimation, and a variety of approaches have been suggested for dealing with them in this context. However, when the focus is on small area estimation using the survey data, much less is known – even though outliers within a small area sample are clearly much more influential than they are in the larger overall sample. To the best of our knowledge, Chambers and Tzavidis (2006) was the first published paper in small area estimation that explicitly addressed the issue of outlier robustness, using an approach based on fitting outlier robust M-quantile models to the survey data. Recently, Sinha and Rao (2009) have also addressed this issue from the perspective of linear mixed models. Both these approaches, however, use plug-in robust prediction. That is, they replace parameter estimates in optimal, but outlier sensitive, predictors by outlier robust versions. Unfortunately, this approach may involve an unacceptable prediction bias (but a low prediction variance) in situations where the outliers are drawn from a distribution that has a different mean to the rest of the survey data (Chambers, 1986), which then leads to the suggestion that outlier robust prediction should include an additional term that makes a correction for this bias. In this paper, we explore the extension of this idea to the small area estimation situation and we propose two different analytical mean squared error (MSE) estimators for outlier robust predictors of small area means. We use simulation based on realistic outlier contaminated data to evaluate how the extended small area estimation approach compares with the plug-in robust methods described earlier. The empirical results show that the biascorrected predictive estimators are less biased than the projective estimators especially when there are outliers in the area effects. Moreover, in the simulation experiments we contrast the proposed MSE estimators with those generally utilized for the plug-in rob

We discuss bias-robust mean squared error estimation for estimators of finite population domain means that can be expressed in pseudo-linear form, i.e. as weighted sums of sample values. Our approach represents an extension of the ideas in Royall and Cumberland (1978) and appears to lead to estimators that are simpler to implement, and potentially more robust, than those suggested in the small area literature. We illustrate the usefulness of our approach through extensive model-based and design-based simulation, with the latter based on two realistic survey data sets containing small area information.

In small area estimation direct survey estimates that rely only on area-specific data can exhibit large sampling variability due to small sample sizes at the small area level. Efficient small area estimates can be constructed using explicit linking models that borrow information from related areas. The most popular class of models for this purpose are models that include random area effects. Estimation for these models typically assumes that the random area effects are uncorrelated. In many situations, however, it is reasonable to assume that the effects of neighbouring areas are correlated. Models that extend conventional random effects models to account for spatial correlation between the small areas have been recently proposed in literature. A new semi-parametric approach to small area estimation is based on the use of M-quantile models. Unlike traditional random effects models, M-quantile models do not depend on strong distributional assumptions and are robust to the presence of outliers. In its current form, however, the M-quantile approach to small area estimation does not allow for spatially correlated area effects. The aim of this paper is to extend the M-quantile approach to account for such spatial correlation between small areas.