Transforming response values in small area prediction

In real application of small area estimation, we often encounter data with positive response values. In this article, we propose the use of parametric transformation for positive response values in the Fay-Herriot model for area-level data. We provide small area predictors and second-order unbiased estimators of mean squared errors for risk evaluation. Through simulation and empirical study, we compare the proposed method with the log-transformed Fay-Herriot model and the conventional Fay-Herriot model, and we show that the proposed method can improve estimation accuracy on two basic models in terms of mean squared errors.