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January, 1980 A Stochastic Ordering Induced by a Concept of Positive Dependence and Monotonicity of Asymptotic Test Sizes
Yosef Rinott, Moshe Pollak
Ann. Statist. 8(1): 190-198 (January, 1980). DOI: 10.1214/aos/1176344901

Abstract

An ordering of distributions related to a concept of positive dependence is studied and stochastic monotonicity with respect to this ordering is established for a wide class of two-sample test statistics. Asymptotic conservativeness of test sizes under certain departures from independence between samples is discussed. For example, if the observations are paired and the joint density is positive semidefinite then tests such as Kolmogorov-Smirnov, $\chi^2$ and Cramer-von Mises, as well as a large class of linear rank tests, are shown to be asymptotically conservative.

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Yosef Rinott. Moshe Pollak. "A Stochastic Ordering Induced by a Concept of Positive Dependence and Monotonicity of Asymptotic Test Sizes." Ann. Statist. 8 (1) 190 - 198, January, 1980. https://doi.org/10.1214/aos/1176344901

Information

Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0428.62013
MathSciNet: MR557564
Digital Object Identifier: 10.1214/aos/1176344901

Subjects:
Primary: 62E10
Secondary: 62E20

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 1 • January, 1980
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