Small Area Estimation with Skewed Data

Abstract

In business surveys, data typically are skewed and the standard approach for small area estimation based on linear mixed models lead to inefficient estimates. In this paper, we discuss small area estimation techniques for skewed data that are linear following a suitable transformation. In this context, implementation of the empirical best linear unbiased prediction (EBLUP) approach under transformation to a linear mixed model is complicated. However, this is not the case with the model-based direct (MBD) approach (Chambers and Chandra, 2006), which is based on weighted linear estimators. We extend the MBD approach to skewed data using sample weights derived via model calibration based on a log transform model with random area effects. Our results show this estimator is both efficient and robust with respect to the distribution of these random effects. An application to real data demonstrates the satisfactory performance of the method