Small Area Estimation for Lognormal Data

This chapter focuses on small area inference methods for a unit level income-type response that is strictly positive and right-skewed. In particular, it compares three predictors based on the assumption that these data follow a lognormal distribution. The three predictors are analogous to a synthetic estimator, a model-based direct estimator, and a best unbiased predictor for the case where the data follow a linear unit-level mixed model on the log scale. The chapter first compares the three predictors and mean squared error (MSE) estimators. Next, it presents an evaluation of the robustness of the empirical best (EB) predictor. The chapter then presents a comparison of the EB predictor for the lognormal model to a predictor based on a gamma distribution. The numerical investigations in the chapter are designed to reflect the properties of data from specific agricultural surveys