ESTIMATION OF A COVARIANCE-MATRIX USING THE REFERENCE PRIOR

• 成果类型: Article
• 署名作者: YANG, RY; BERGER, JO
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325625
• 发表日期: 1994
• 页码: 1195-1211
• 关键词: Empirical Bayes; minimax estimators; precision matrix; distributions; inference; IDENTITY

摘要

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.