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Estimation of covariance matrices based on hierarchical inverse-Wishart priors. (English) Zbl 1428.62216

Summary: This paper focuses on Bayesian shrinkage methods 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 conditions for the existence 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.

MSC:

62H12 Estimation in multivariate analysis
62E15 Exact distribution theory in statistics
62F15 Bayesian inference
62J07 Ridge regression; shrinkage estimators (Lasso)