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November, 1975 On Re-Pairing Observations in a Broken Random Sample
Prem K. Goel
Ann. Statist. 3(6): 1364-1369 (November, 1975). DOI: 10.1214/aos/1176343292

Abstract

It is assumed that a random sample of size $n$ is drawn from a bivariate distribution $f(t, u)$ which possesses a monotone likelihood ratio (MLR). However, before the sample values are observed, the pairs are `broken' into components $t$ and $u$. Therefore, the original sample pairings are unknown, and it is desired to optimally re-pair $t$- and $u$-values in order to reconstruct the original bivariate sample. It is observed that for the maximum likelihood pairing (MLP) to be the `natural' pairing for all $t$- and $u$-values, it is necessary that $f$ has MLR. It is shown that if it is desired to maximize the expected number of correct matches, then the class of procedures $\Phi_{1, n}$, which result in pairing the largest $t$ with the largest $u$ and the smallest $t$ with the smallest $u$, is a complete class. A sufficient condition under which the MLP maximizes the expected number of correct matches is also obtained.

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Prem K. Goel. "On Re-Pairing Observations in a Broken Random Sample." Ann. Statist. 3 (6) 1364 - 1369, November, 1975. https://doi.org/10.1214/aos/1176343292

Information

Published: November, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0319.62003
MathSciNet: MR386076
Digital Object Identifier: 10.1214/aos/1176343292

Subjects:
Primary: 62C07
Secondary: 62P99

Keywords: Broken random sample , complete class , Matching , monotone likelihood pairing , monotone likelihood ratio

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 6 • November, 1975
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