Transforming response values in small area prediction

TL;DR

This paper proposes a parametric transformation within the Fay-Herriot model for small area estimation with positive responses, deriving an unbiased predictor and MSE estimator, validated through simulations and real data application.

Contribution

It introduces a novel parametric transformation approach for small area prediction with positive data, including unbiased prediction and MSE estimation methods.

Findings

The proposed predictor is asymptotically unbiased.

The MSE estimator is second-order unbiased via bootstrap.

The method performs well in simulations and real data application.

Abstract

In real applications of small area estimation, one often encounters data with positive response values. The use of a parametric transformation for positive response values in the Fay-Herriot model is proposed for such a case. An asymptotically unbiased small area predictor is derived and a second-order unbiased estimator of the mean squared error is established using the parametric bootstrap. Through simulation studies, a finite sample performance of the proposed predictor and the MSE estimator is investigated. The methodology is also successfully applied to Japanese survey data.