The Annals of Mathematical Statistics

Inadmissibility of a Class of Estimators of a Normal Quantile

James V. Zidek

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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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Ann. Math. Statist., Volume 42, Number 4 (1971), 1444-1447.

First available in Project Euclid: 27 April 2007

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Zidek, James V. Inadmissibility of a Class of Estimators of a Normal Quantile. Ann. Math. Statist. 42 (1971), no. 4, 1444--1447. doi:10.1214/aoms/1177693258.

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