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) |