Estimation of a Covariance Matrix Using the Reference Prior

Yang, Ruoyong ; Berger, James O.

Ann. Statist., Tome 22 (1994) no. 1, p. 1195-1211 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1994-09-14
Classification:  Jeffreys prior,  reference prior,  covariance matrix,  information matrix,  Markov chain simulation,  hit-and-run sampler,  entropy loss,  quadratic loss,  risk,  62C10,  62F15,  62H12