Abstract #301168


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JSM 2002 Abstract #301168
Activity Number: 284
Type: Contributed
Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Stat. Sciences*
Abstract - #301168
Title: On Comparing Bayes Estimators to the Sample Mean in Multivariate Normal Problems
Author(s): Eric Vestrup*+
Affiliation(s): DePaul University
Address: 2320 North Kenmore, Chicago, Illinois, 60614, USA
Keywords: multivariate normal distribution ; squared error loss ; mean-correct priors ; Bayes risk
Abstract:

In estimating the mean of a bivariate normal distribution, both the sample mean and the Bayes rule relative to a conjugate normal prior are admissible and viable estimators. In this paper, a comparison of their performance is executed, leading to a general discussion of the circumstances under which a Bayes rule tends to outperform the sample mean. As in Samaniego and Reneau (1994), the Bayes risk relative to a separate "true'' prior distribution is used as the performance criterion. An extension to a more general Bayesian framework, which includes a random covariance matrix modeled by an inverted Wishart distribution, is also treated. All derivations are carried out in arbitrary dimension k > 1, but the problem considered is of particular interest when k = 2.


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