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

Estimation of covariance matrices based on hierarchical inverse-Wishart priors