Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices

TL;DR

This paper introduces a non-parametric shrinkage estimator for the population mean under quadratic loss, effective even with unknown covariance matrices, and demonstrates its advantages through simulations and real data analysis.

Contribution

It proposes a novel non-parametric shrinkage estimator that does not rely on parametric assumptions or prior covariance information, improving mean estimation in high-dimensional settings.

Findings

The estimator outperforms existing methods in simulations.

Asymptotic properties are established for the estimator.

Practical benefits are shown through real data applications.

Abstract

In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric distribution for the data and it does not require the prior information on the population covariance matrix. Analytical results on the improvement of the proposed shrinkage estimator are provided and some corresponding asymptotic properties are also derived. Finally, we demonstrate the practical improvement of the proposed method over existing methods through extensive simulation studies and real data analysis. Keywords: High-dimensional data; Shrinkage estimator; Large $p$ small $n$; $U$-statistic.