On the minimax estimator of a bounded normal mean

Éric Marchand and François Perron

Statistics & Probability Letters, 2002, vol. 58, issue 4, 327-333

Abstract: For estimating under squared-error loss the mean of a p-variate normal distribution when this mean lies in a ball of radius m centered at the origin and the covariance matrix is equal to the identity matrix, it is shown that the Bayes estimator with respect to a uniformly distributed prior on the boundary of the parameter space ([delta]BU) is minimax whenever . Further descriptions of the cutoff points of small enough radiuses (i.e., m[less-than-or-equals, slant]m0(p)) for [delta]BU to be minimax are given. These include lower bounds and the large dimension p limiting behaviour of . Finally, implications for the associated minimax risk are described.

Keywords: Minimax; estimator; Restricted; parameter; space; Multivariate; normal; distribution; Squared; error; loss (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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