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September, 1984 A Sharp Necessary and Sufficient Condition for Inadmissibility of Estimators in a Control Problem
C. Srinivasan
Ann. Statist. 12(3): 927-944 (September, 1984). DOI: 10.1214/aos/1176346712

Abstract

Suppose $\mathbf{x} = (x_1, \cdots, x_m)^t$ is an $m$-variate normal random variable with mean vector $\mathbf{\theta} = (\theta_1, \cdots, \theta_m)^t$ and identity dispersion matrix. We consider the control problem which, in canonical form, is the problem of estimating $\mathbf{\theta}$ with respect to the loss $L(\theta, \delta) = (1 - \theta^t\delta)^2,$ where $\delta(x) = (\delta_1(x), \cdots, \delta_m(x))^t$. A necessary and sufficient condition for the admissibility of spherically symmetric generalized Bayes $\delta(x)$ is given in terms of a Dirichlet problem. This condition is also equivalent to recurrence of a diffusion process and insolubility of certain elliptic boundary value problems.

Citation

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C. Srinivasan. "A Sharp Necessary and Sufficient Condition for Inadmissibility of Estimators in a Control Problem." Ann. Statist. 12 (3) 927 - 944, September, 1984. https://doi.org/10.1214/aos/1176346712

Information

Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0547.62006
MathSciNet: MR751283
Digital Object Identifier: 10.1214/aos/1176346712

Subjects:
Primary: 62C15
Secondary: 62F10, 62P20

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • September, 1984
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