Small Area Predictors with Dual Shrinkage of Means and Variances

TL;DR

This paper introduces a closed-form approximated empirical Bayes estimator for small-area estimation with random dispersions, enabling efficient computation and improved accuracy in modeling area-specific means and variances.

Contribution

It proposes a novel closed-form AEB estimator for models with random dispersions, along with methods for parameter estimation and MSE evaluation.

Findings

The AEB estimator provides accurate estimates with a closed-form expression.

The method effectively estimates model parameters via the moment method.

The bootstrap approach accurately assesses the mean squared error.

Abstract

The paper concerns small-area estimation in the Fay-Herriot type area-level model with random dispersions, which models the case that the sampling errors change from area to area. The resulting Bayes estimator shrinks both means and variances, but needs numerical computation to provide the estimates. In this paper, an approximated empirical Bayes (AEB) estimator with a closed form is suggested. The model parameters are estimated via the moment method, and the mean squared error of the AEB is estimated via the single parametric bootstrap method. The benchmarked estimator and a second-order unbiased estimator of the mean squared error are also derived.