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 robust predictors. The proposed bias-robust and linearization-based MSE estimators appear to perform well when used with the robust predictors of small area means that are considered in this paper.

The National Sample Survey Organisation (NSSO) surveys are the main source of official statistics in India and generate a range of invaluable data at the macro level (e.g. state and national level). However, the NSSO data cannot be used directly to produce reliable estimates at the micro level (e.g. district or further disaggregate level) due to small sample sizes. There is a rapidly growing demand of such micro level statistics in India as the country is moving from centralized to more decentralized planning system. In this article we employ small area estimation (SAE) techniques to derive model-based estimates of proportion of indebted households at district or at other small area levels in the State of not possible to produce estimates using sample data alone. The model based estimates generated using SAE are still reliable for such areas. The estimates are expected to provide invaluable information to policy-analysts and decision-makers.

In this paper a geographical weighted pseudo empirical best linear unbiased predictor (GWEBLUP) for small area averages is proposed, and two approaches for estimating its mean squared error (MSE), a conditional approach and an unconditional one, are developed. The popular empirical best linear unbiased predictor (EBLUP) under the linear mixed model and its associated MSE estimator are obtained as a special case of the GWEBLUP. Empirical results using both model-based and design-based simulations, with the latter based on two real data sets, show that the GWEBLUP predictor can lead to efficiency gains when spatial nonstationarity is present in the data. A practical gain from using the GWEBLUP is in small area estimation for out of sample areas. In this case the efficient use of geographical information can potentially improve upon conventional synthetic estimation.

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Raymond CHAMBERS and Hukum CHANDRA Random effects models for hierarchically dependent data, for example, clustered data, are widely used. A popular bootstrap method for such data is the parametric bootstrap based on the same random effects model as that used in inference. However, it is hard to justify this type of bootstrap when this model is known to be an approximation. In this article, we describe a random effect block bootstrap approach for clustered data that is simple to implement, free of both the distribution and the dependence assumptions of the parametric bootstrap, and is consistent when the mixed model assumptions are valid. Results based on Monte Carlo simulation show that the proposed method seems robust to failure of the dependence assumptions of the assumed mixed model. An application to a realistic environmental dataset indicates that the method produces sensible results. Supplementary materials for the article, including the data used for the application, are available online.

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There is a growing need for current and reliable counts at small area level. The empirical predictor under a generalized linear mixed model (GLMM) is often used for small area estimation (SAE) of such counts. However, the fixed effect parameters of a GLMM are spatially invariant and do not account for the presence of spatial nonstationarity in the population of interest. A geographically weighted regression extension of the GLMM is developed, extending this model to allow for spatial nonstationarity, and SAE based on this spatially nonstationary model (NSGLMM) is described. The empirical predictor for small area counts (NSEP) under an area level NSGLMM is proposed. Analytic and bootstrap approaches to estimating the mean squared error of the NSEP are also developed, and a parametric approach to testing for spatial nonstationarity is described. The approach is illustrated by applying it to a study of poverty mapping using socio- economic survey data from India

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