Shrinkage estimation of a mean matrix of a multivariate complex normal distribution

TL;DR

This paper develops minimax shrinkage estimators for the mean matrix of a multivariate complex normal distribution with unknown covariance, using advanced identities and eigenvalue calculus to evaluate risk.

Contribution

It introduces new minimax shrinkage estimators for complex normal mean matrices, extending classical methods with complex identities and eigenvalue techniques.

Findings

Derived an unbiased risk estimate for invariant estimators.

Constructed several minimax shrinkage estimators.

Provided theoretical risk bounds and optimality results.

Abstract

The problem of estimating a mean matrix of a multivariate complex normal distribution with an unknown covariance matrix is considered under an invariant loss function. By using complex versions of the Stein identity, the Stein-Haff identity, and calculus on eigenvalues, a formula is obtained for an unbiased estimate of the risk of an invariant class of estimators, from which several minimax shrinkage estimators are constructed.