The Annals of Statistics

A Stochastic Ordering Induced by a Concept of Positive Dependence and Monotonicity of Asymptotic Test Sizes

Yosef Rinott and Moshe Pollak

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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.

Article information

Source
Ann. Statist., Volume 8, Number 1 (1980), 190-198.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344901

Digital Object Identifier
doi:10.1214/aos/1176344901

Mathematical Reviews number (MathSciNet)
MR557564

Zentralblatt MATH identifier
0428.62013

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62E20: Asymptotic distribution theory

Keywords
Stochastic ordering positive dependence two-sample test conservativeness convexity Gaussian processes total positivity

Citation

Rinott, Yosef; Pollak, Moshe. A Stochastic Ordering Induced by a Concept of Positive Dependence and Monotonicity of Asymptotic Test Sizes. Ann. Statist. 8 (1980), no. 1, 190--198. doi:10.1214/aos/1176344901. https://projecteuclid.org/euclid.aos/1176344901


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