Optimal shrinkage estimation in heteroscedastic hierarchical linear models

TL;DR

This paper develops and analyzes optimal shrinkage estimators for heteroscedastic hierarchical linear models, demonstrating their asymptotic optimality and superior performance through simulations and real data applications.

Contribution

It introduces a class of parametric and semiparametric shrinkage estimators based on unbiased risk estimate for heteroscedastic hierarchical models, establishing their asymptotic optimality.

Findings

Proposed estimators outperform existing methods in simulations.

Estimates achieve asymptotic optimality under mean squared error.

Real data application shows practical effectiveness.

Abstract

Shrinkage estimators have profound impacts in statistics and in scientific and engineering applications. In this article, we consider shrinkage estimation in the presence of linear predictors. We formulate two heteroscedastic hierarchical regression models and study optimal shrinkage estimators in each model. A class of shrinkage estimators, both parametric and semiparametric, based on unbiased risk estimate (URE) is proposed and is shown to be (asymptotically) optimal under mean squared error loss in each model. Simulation study is conducted to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging and interesting results.