Restricted risk Bayes estimation for the mean of the multivariate normal distribution

Shun-Yu Chen

Journal of Multivariate Analysis, 1988, vol. 24, issue 2, 207-217

Abstract: Let X = (X1,...,Xp)t to be an observation from a p-variate normal distribution with unknown mean vector [theta] = ([theta]1,...,[theta]p)t and known covariance matrix [Sigma]. It is desired to estimate [theta] under the quadratic loss L([theta], [delta]) = ([theta] - [delta])tQ([theta] - [delta]). Suppose prior beliefs concerning [theta] can be approximately modeled by a conjugate prior distribution [pi] which is Np([mu], A), where [mu] and A are known. We find estimators of [theta] which have small Bayes risk and which also satisfy the constraint R([theta], [delta])

Keywords: risk; Bayes; risk; relative; saving; risk (search for similar items in EconPapers)
Date: 1988
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