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January, 1973 On a Minimax Estimate for the Mean of a Normal Random Vector Under a Generalized Quadratic Loss Function
Tamer Basar, Max Mintz
Ann. Statist. 1(1): 127-134 (January, 1973). DOI: 10.1214/aos/1193342388

Abstract

An admissible minimax estimate for the mean of a normal random vector with known covariance is derived for a generalized quadratic loss function. This loss function is quadratic in both the estimation error and the unknown mean. The estimate is derived using the method of least favorable prior distributions. The decision rule is linear, and the least favorable prior distribution for the unknown mean is normal with zero mean. The covariance of this least favorable normal distribution is determined by the solution of a certain nonlinear algebraic matrix equation.

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Tamer Basar. Max Mintz. "On a Minimax Estimate for the Mean of a Normal Random Vector Under a Generalized Quadratic Loss Function." Ann. Statist. 1 (1) 127 - 134, January, 1973. https://doi.org/10.1214/aos/1193342388

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0253.62021
MathSciNet: MR336860
Digital Object Identifier: 10.1214/aos/1193342388

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 1 • January, 1973
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