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April, 1995 Admissibility and Minimaxity of the UMVU Estimator of $P\{X < Y\}$
Qiqing Yu, Z. Govindarajulu
Ann. Statist. 23(2): 598-607 (April, 1995). DOI: 10.1214/aos/1176324538

Abstract

Suppose that $X_1,\ldots, X_m$ are i.i.d. from a continuous distribution function $F$ and $Y_1,\ldots, Y_n$ are i.i.d. from a continuous distribution function $G; X$'s and $Y$'s are independent. A minimum variance unbiased estimator of $P\{X < Y\}$ is the Mann-Whitney statistic. We show that the Mann-Whitney statistic is admissible under a class of weighted squared error losses and is minimax under a proper weighted squared error loss.

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Qiqing Yu. Z. Govindarajulu. "Admissibility and Minimaxity of the UMVU Estimator of $P\{X < Y\}$." Ann. Statist. 23 (2) 598 - 607, April, 1995. https://doi.org/10.1214/aos/1176324538

Information

Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0824.62008
MathSciNet: MR1332584
Digital Object Identifier: 10.1214/aos/1176324538

Subjects:
Primary: 62C15
Secondary: 62C10

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 2 • April, 1995
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