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December, 1987 Estimating the Mean of a Normal Distribution with Loss Equal to Squared Error Plus Complexity Cost
Peter J. Kempthorne
Ann. Statist. 15(4): 1389-1400 (December, 1987). DOI: 10.1214/aos/1176350600

Abstract

Estimating the mean of a $p$-variate normal distribution is considered when the loss is squared error plus a complexity cost. The complexity of estimates is defined using a partition of the parameter space into sets corresponding to models of different complexity. The model implied by the use of an estimate determines the estimate's complexity cost. Complete classes of estimators are developed which consist of preliminary-test estimators. As is the case when loss is just squared error, the maximum-likelihood estimator is minimax. However, unlike the no-complexity-cost case, the maximum-likelihood estimator is inadmissible even in the case when $p = 1$ or 2.

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Peter J. Kempthorne. "Estimating the Mean of a Normal Distribution with Loss Equal to Squared Error Plus Complexity Cost." Ann. Statist. 15 (4) 1389 - 1400, December, 1987. https://doi.org/10.1214/aos/1176350600

Information

Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0629.62009
MathSciNet: MR913564
Digital Object Identifier: 10.1214/aos/1176350600

Subjects:
Primary: 62C07
Secondary: 62C20

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 4 • December, 1987
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