  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.
