The Annals of Statistics

Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss

Ann Cohen Brandwein and William E. Strawderman

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 8, Number 2 (1980), 279-284.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344953

Digital Object Identifier
doi:10.1214/aos/1176344953

Mathematical Reviews number (MathSciNet)
MR560729

Zentralblatt MATH identifier
0432.62008

JSTOR
links.jstor.org

Subjects
Primary: 62C99: None of the above, but in this section
Secondary: 62F10: Point estimation 62H99: None of the above, but in this section

Keywords
Minimax estimation spherically symmetric multivariate location parameter

Citation

Brandwein, Ann Cohen; Strawderman, William E. Minimax Estimation of Location Parameters for Spherically Symmetric Distributions with Concave Loss. Ann. Statist. 8 (1980), no. 2, 279--284. doi:10.1214/aos/1176344953. https://projecteuclid.org/euclid.aos/1176344953


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