Parametric Transformed Fay-Herriot Model for Small Area Estimation

TL;DR

This paper introduces a parametric transformed Fay-Herriot model for small area estimation, establishing conditions for estimator consistency, deriving prediction error approximations, and validating through simulations and empirical data.

Contribution

It provides a comprehensive framework for transformed Fay-Herriot models, including conditions for estimator consistency and second-order prediction error approximation.

Findings

Dual power transformation satisfies the consistency conditions.

Derived second-order unbiased estimator of prediction error.

Simulation and empirical studies demonstrate the effectiveness of the proposed methods.

Abstract

In this paper, we consider parametric transformed Fay-Herriot models, and clarify conditions on transformations under which the estimator of the transformation is consistent. It is shown that the dual power transformation satisfies the conditions. Based on asymptotic properties for estimators of parameters, we derive a second-order approximation of the prediction error of the empirical best linear unbiased predictors (EBLUP) and obtain a second-order unbiased estimator of the prediction error. Finally, performances of the proposed procedures are investigated through simulation and empirical studies.