Polynomials shrinkage estimators of a multivariate normal mean

TL;DR

This paper investigates polynomial shrinkage estimators for multivariate normal means, demonstrating their minimax properties and how increasing polynomial degree improves estimation performance.

Contribution

It introduces polynomial form shrinkage estimators that outperform traditional estimators and shows how higher-degree polynomials enhance estimation accuracy.

Findings

Polynomial estimators dominate MLE under certain conditions.

Increasing polynomial degree improves estimator performance.

Shrinkage estimators are minimax under specified conditions.

Abstract

In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering estimators that generalize the James-Stein estimator and show that these estimators dominate the maximum likelihood estimator (MLE), therefore are minimax, when the shrinkage function satisfies some conditions. Then, we treat estimators of polynomial form and prove the increase of the degree of the polynomial allows us to build a better estimator from the one previously constructed.