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Estimation of a covariance matrix using the reference prior. (English) Zbl 0819.62013
Summary: Estimation of a covariance matrix \(\Sigma\) is a notoriously difficult problem; the standard unbiased estimator can be substantially suboptimal. We approach the problem from a noninformative prior Bayesian perspective, developing the reference noninformative prior for a covariance matrix and obtaining expressions for the resulting Bayes estimators. These expressions involve the computation of high-dimensional posterior expectations, which is done using a recent Markov chain simulation tool, the hit-and-run sampler. Frequentist risk comparisons with previously suggested estimators are also given, and determination of the accuracy of the estimators is addressed.

62C10 Bayesian problems; characterization of Bayes procedures
62H12 Estimation in multivariate analysis
62F15 Bayesian inference
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