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June, 1991 Shrinkage Domination in a Multivariate Common Mean Problem
Edward I. George
Ann. Statist. 19(2): 952-960 (June, 1991). DOI: 10.1214/aos/1176348130


Consider the problem of estimating the $p \times 1$ mean vector $\theta$ under expected squared error loss, based on the observation of two independent multivariate normal vectors $Y_1 \sim N_p(\theta, \sigma^2I)$ and $Y_2 \sim N_p(\theta, \lambda\sigma^2I)$ when $\lambda$ and $\sigma^2$ are unknown. For $p \geq 3$, estimators of the form $\delta_\eta = \eta Y_1 + (1 - \eta)Y_2$ where $\eta$ is a fixed number in (0, 1), are shown to be uniformly dominated in risk by Stein estimators in spite of the fact that independent estimates of scale are unavailable. A consequence of this result is that when $\lambda$ is assumed known, shrinkage domination is robust to incorrect specification of $\lambda$.


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Edward I. George. "Shrinkage Domination in a Multivariate Common Mean Problem." Ann. Statist. 19 (2) 952 - 960, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0725.62051
MathSciNet: MR1105854
Digital Object Identifier: 10.1214/aos/1176348130

Primary: 62H12
Secondary: 62C99 , 62J07

Keywords: risk , robustness , shrinkage estimation , Stein estimators

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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