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April, 1995 A Note on Admissibility When Precision is Unbounded
Charles Anderson, Nabendu Pal
Ann. Statist. 23(2): 593-597 (April, 1995). DOI: 10.1214/aos/1176324537

Abstract

The estimation of a common mean vector $\theta$ given two independent normal observations $X \sim N_p(\theta, \sigma^2_x I)$ and $Y \sim N_p(\theta, \sigma^2_y I)$ is reconsidered. It being known that the estimator $\eta X + (1 - \eta)Y$ is inadmissible when $\eta \in (0, 1)$, we show that when $\eta$ is 0 or 1, then the opposite is true, that is, the estimator is admissible. The general situation is that an estimator $X^\ast$ can be improved by shrinkage when there exists a statistic $B$ which, in a certain sense, estimates a lower bound on the risk of $X^\ast$. On the other hand, an estimator is admissible under very general conditions if there is no reasonable way to detect that its risk is small.

Citation

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Charles Anderson. Nabendu Pal. "A Note on Admissibility When Precision is Unbounded." Ann. Statist. 23 (2) 593 - 597, April, 1995. https://doi.org/10.1214/aos/1176324537

Information

Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0824.62007
MathSciNet: MR1332583
Digital Object Identifier: 10.1214/aos/1176324537

Subjects:
Primary: 62C15
Secondary: 62H12

Keywords: inadmissibility , shrinkage estimation , Stein's normal identity

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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