Estimation of covariance matrices based on hierarchical inverse-Wishart priors

TL;DR

This paper investigates Bayesian covariance matrix estimation using hierarchical inverse-Wishart priors, analyzing posterior properties, risks, and demonstrating their effectiveness through simulations under different loss functions.

Contribution

It introduces new hierarchical inverse-Wishart priors for covariance estimation and studies their theoretical properties and practical performance.

Findings

Posterior distributions exist under certain conditions.

Hierarchical priors improve estimation accuracy.

Simulation results show advantages over traditional methods.

Abstract

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence conditions of the posterior distributions. Advantages in terms of numerical simulations of posteriors are shown. A simulation study illustrates the performance of the estimation procedures under three loss functions for relevant sample sizes and various covariance structures.