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March, 1980 Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss
Ann Cohen Brandwein, William E. Strawderman
Ann. Statist. 8(2): 279-284 (March, 1980). DOI: 10.1214/aos/1176344953

Abstract

For $p \geqslant 4$ and one observation $X$ on a $p$-dimensional spherically symmetric distribution, minimax estimators of $\theta$ whose risks are smaller than the risk of $X$ (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For $n$ observations $X_1, X_2, \cdots, X_n$, we have classes of minimax estimators which are better than the usual procedures, such as the best invariant estimator, $\bar{X}$, or a maximum likelihood estimator.

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Ann Cohen Brandwein. William E. Strawderman. "Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss." Ann. Statist. 8 (2) 279 - 284, March, 1980. https://doi.org/10.1214/aos/1176344953

Information

Published: March, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0432.62008
MathSciNet: MR560729
Digital Object Identifier: 10.1214/aos/1176344953

Subjects:
Primary: 62C99
Secondary: 62F10, 62H99

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 2 • March, 1980
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