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July, 1973 On a Multiple Decision Rule
Khursheed Alam
Ann. Statist. 1(4): 750-755 (July, 1973). DOI: 10.1214/aos/1176342470


Let $X = (X_1, \cdots, X_k)$ be a random vector whose distribution depends on a parameter vector $\theta = (\theta_1, \cdot, \theta_k)$. A standard procedure $\phi^\ast$ is considered for selecting a set of $m < k$ coordinate values corresponding to the $m$ largest components of $\theta$. $\phi^\ast$ is given as follows: Select the $m$ coordinates corresponding to the $m$ largest components of $x$, the observed value of $X$. Break ties, if any, with randomization. Some optimal properties of $\phi^\ast$ are known, given that the loss function and the distribution of $X$ have certain invariance and monotonicity properties. It is shown in this paper that $\phi^\ast$ is a Bayes decision rule if $X$ is "stochastically increasing" in $\theta$.


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Khursheed Alam. "On a Multiple Decision Rule." Ann. Statist. 1 (4) 750 - 755, July, 1973.


Published: July, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0263.62002
MathSciNet: MR345257
Digital Object Identifier: 10.1214/aos/1176342470

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 4 • July, 1973
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