Outlier Robust Small Area Estimation

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.