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Abstract:
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Statistical agencies are often asked to produce small area estimates for skewed variables. When domain sample sizes are too small to support direct estimators, the effect of skewness of the response variable can be large. As such, it is important to appropriately account for the distribution of the response variable given available auxiliary information with measurement errors. Motivated by this issue, we first stabilize the skewness to achieve normality in the response variable, and we propose an area-level log-measurement error model on the response variable. Second, under our proposed modeling framework, we derive an adjusted empirical Bayes (EB) predictor of positive small area quantities subject to the covariates containing measurement error. Third, we propose a corresponding mean squared prediction error (MSPE) using a jackknife method and a bootstrap method, where we illustrate that the order of the bias is O(1/m) with m as the total number of small areas. Fourth, we illustrate our methodology using both design-based and model-based simulation studies.
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