The Annals of Statistics

Estimation of a Covariance Matrix Using the Reference Prior

Ruoyong Yang and James O. Berger

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325625

Digital Object Identifier
doi:10.1214/aos/1176325625

Mathematical Reviews number (MathSciNet)
MR1311972

Zentralblatt MATH identifier
0819.62013

JSTOR
links.jstor.org

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176325625


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