Small Area Estimation under Square Root Transformed Fay-Herriot model with Functional Measurement Error in Covariates

TL;DR

This paper develops a new small area estimation method under square-root transformation accounting for functional measurement error, proposing predictors that rely only on observed data and secondary survey information.

Contribution

It introduces a novel predictor for small area estimation with measurement error, avoiding dependence on unobservable covariates, and discusses parameter estimation methods.

Findings

The proposed predictor performs well in simulations.

Performance depends on the number of areas and secondary survey size.

The method effectively handles functional measurement error.

Abstract

We consider a small area estimation model under square-root transformation in the presence of functional measurement error. When measurement error is present, the Bayes predictor can no longer be used as it depends on the covariates even if parameters are known. Therefore suitable replacements are called for, and we propose a predictor that only depends on observed responses and data obtained from a large secondary survey. Moreover, some estimating methods of unknown parameters are considered. In the simulations section, We evaluate the performance using the mean squared prediction error (MSPE) and discuss several scenarios in terms of the number of areas and the sample size in a large secondary survey.