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April 2020 Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale
Yuzo Maruyama, William E. Strawderman
Ann. Statist. 48(2): 1052-1071 (April 2020). DOI: 10.1214/19-AOS1837

Abstract

This paper investigates estimation of the mean vector under invariant quadratic loss for a spherically symmetric location family with a residual vector with density of the form $f(x,u)=\eta ^{(p+n)/2}f(\eta \{\|x-\theta \|^{2}+\|u\|^{2}\})$, where $\eta $ is unknown. We show that the natural estimator $x$ is admissible for $p=1,2$. Also, for $p\geq 3$, we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators of the form $\{1-\xi (x/\|u\|)\}x$. In the Gaussian case, a variant of the James–Stein estimator, $[1-\{(p-2)/(n+2)\}/\{\|x\|^{2}/\|u\|^{2}+(p-2)/(n+2)+1\}]x$, which dominates the natural estimator $x$, is also admissible within this class. We also study the related regression model.

Citation

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Yuzo Maruyama. William E. Strawderman. "Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale." Ann. Statist. 48 (2) 1052 - 1071, April 2020. https://doi.org/10.1214/19-AOS1837

Information

Received: 1 September 2018; Revised: 1 March 2019; Published: April 2020
First available in Project Euclid: 26 May 2020

zbMATH: 07241580
MathSciNet: MR4102687
Digital Object Identifier: 10.1214/19-AOS1837

Subjects:
Primary: 62C15
Secondary: 62J07

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 2 • April 2020
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