The Annals of Statistics

Estimation of a Covariance Matrix Using the Reference Prior

Ruoyong Yang and James O. Berger

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Estimation of a covariance matrix $\sum$ 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.

Article information

Ann. Statist., Volume 22, Number 3 (1994), 1195-1211.

First available in Project Euclid: 11 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62F15: Bayesian inference 62H12: Estimation

Jeffreys prior reference prior covariance matrix information matrix Markov chain simulation hit-and-run sampler entropy loss quadratic loss risk


Yang, Ruoyong; Berger, James O. Estimation of a Covariance Matrix Using the Reference Prior. Ann. Statist. 22 (1994), no. 3, 1195--1211. doi:10.1214/aos/1176325625.

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