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August, 1971 Inadmissibility of a Class of Estimators of a Normal Quantile
James V. Zidek
Ann. Math. Statist. 42(4): 1444-1447 (August, 1971). DOI: 10.1214/aoms/1177693258


Suppose that independent normally distributed random vectors $W^{n\times 1}$ and $T^{k\times 1}$ are observed with $E(W) = 0, E(T) = \mu, \operatorname{Cov} (W) = \sigma^2 I$ and $\operatorname{Cov} (T) = \sigma^2 I$. In this paper it is shown that each member of a certain class of estimators of $\mu + \eta\sigma$ for a given vector $\eta$ is inadmissible if loss is dimension-free quadratic loss. This class includes the best invariant estimator. The proof is carried out by exhibiting, for each member, $\hat{\theta}$, of the class, an estimator depending on $\hat{\theta}$ whose risk is uniformly smaller than that of $\hat{\theta}$.


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James V. Zidek. "Inadmissibility of a Class of Estimators of a Normal Quantile." Ann. Math. Statist. 42 (4) 1444 - 1447, August, 1971.


Published: August, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0225.62036
MathSciNet: MR287637
Digital Object Identifier: 10.1214/aoms/1177693258

Rights: Copyright © 1971 Institute of Mathematical Statistics

Vol.42 • No. 4 • August, 1971
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