Second-order unbiased naive estimator of mean squared error for EBLUP in small-area estimation

TL;DR

This paper introduces a new adjusted maximum-likelihood method to produce a naive MSE estimator for EBLUP in small-area estimation that is second-order unbiased, improving accuracy over existing naive estimators.

Contribution

It develops a novel adjusted maximum-likelihood approach to obtain a naive MSE estimator with second-order unbiasedness for EBLUP, enhancing small-area estimation inference.

Findings

The new method achieves second-order unbiasedness.

It remedies the underestimation of existing naive estimators.

Simulation results confirm improved performance.

Abstract

An empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in small-area estimation. To measure its uncertainty, we need to estimate its mean squared error (MSE) since the true MSE cannot generally be derived in a closed form. The "naive MSE estimator", one of the estimators available for small-area inference, is unlikely to be chosen, since it does not achieve the desired asymptotic property, namely second-order unbiasedness, although it maintains strict positivity and tractability. Therefore, users tend to choose the second-order unbiased MSE estimator. In this paper, we seek a new adjusted maximum-likelihood method to obtain a naive MSE estimator that achieves the required asymptotic property. To obtain the result, we also reveal the relationship between the general adjusted maximum-likelihood method for the model variance parameter and the general functional form of the second-order unbiased, and strictly positive, MSE estimator. We also compare the performance of the new method with that of the existing naive estimator through a Monte Carlo simulation study. The results show that the new method remedies the underestimation associated with the existing naive estimator.