l_p-norm based James-Stein estimation with minimaxity and sparsity

TL;DR

This paper introduces a new class of minimax Stein-type estimators for multivariate normal means that utilize an l_p norm-based shrinkage factor, enabling sparse estimation by setting some coordinates to zero while maintaining minimax properties.

Contribution

It proposes a novel l_p norm-based shrinkage estimator that achieves both sparsity and minimaxity in multivariate normal mean estimation.

Findings

The estimators allow some coordinates to be exactly zero.

They maintain minimax risk properties.

They provide a flexible framework for sparse estimation.

Abstract

A new class of minimax Stein-type shrinkage estimators of a multivariate normal mean is studied where the shrinkage factor is based on an l_p norm. The proposed estimators allow some but not all coordinates to be estimated by 0 thereby allow sparsity as well as minimaxity.