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October, 1971 Admissibility of Certain Location Invariant Multiple Decision Procedures
Martin Fox
Ann. Math. Statist. 42(5): 1553-1561 (October, 1971). DOI: 10.1214/aoms/1177693153


Random variables $X, Y_1, Y_2, \cdots$ are available for observation with $X$ real valued and $Y_1, Y_2, \cdots$ taking values in arbitrary spaces. The distribution of $Y = (Y_1, Y_2, \cdots)$ is given by $\mu_j (j = 1, \cdots, r)$ and the conditional density with respect to Lebesgue measure given $Y_i = y_i(i = 1, \cdots, n - 1)$ is $p_{jn}(x - \theta, y)$ where $y = (y_1, y_2, \cdots)$. The parameters $j$ and $\theta$ are unknown. A decision $k \in \{1, \cdots, m\}$ is to be made with loss $W(j, k, n, y)$ when $n$ observations are taken. Following Brown's (1966) methods admissibility is proved for the decision procedure which is Bayes in the class of invariant procedures. The result contains that of Lehmann and Stein (1953).


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Martin Fox. "Admissibility of Certain Location Invariant Multiple Decision Procedures." Ann. Math. Statist. 42 (5) 1553 - 1561, October, 1971.


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

zbMATH: 0238.62009
MathSciNet: MR397941
Digital Object Identifier: 10.1214/aoms/1177693153

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 5 • October, 1971
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