Open Access
December 1998 Directional tests for one-sided alternatives in multivariate models
Arthur Cohen, Harold B. Sackrowitz
Ann. Statist. 26(6): 2321-2338 (December 1998). DOI: 10.1214/aos/1024691473

Abstract

Consider one-sided testing problems for a multivariate exponential family model. Through conditioning or other considerations, the problem oftentimes reduces to testing a null hypothesis that the natural parameter is a zero vector against the alternative that the natural parameter lies in a closed convex cone $\mathscr{C}$. The problems include testing homogeneity of parameters, testing independence in contingency tables, testing stochastic ordering of distributions and many others. A test methodology is developed that directionalizes the usual test procedures such as likelihood ratio, chi square, Fisher, and so on. The methodology can be applied to families of tests where the family is indexed by a size parameter so as to enable nonrandomized testing by $p$-values. For discrete models, a refined family of tests provides a refined grid for better testing by $p$-values. The tests have essential monotonicity properties that are required for admissibility and for desirable power properties. Two examples are given.

Citation

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Arthur Cohen. Harold B. Sackrowitz. "Directional tests for one-sided alternatives in multivariate models." Ann. Statist. 26 (6) 2321 - 2338, December 1998. https://doi.org/10.1214/aos/1024691473

Information

Published: December 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0927.62056
MathSciNet: MR1700234
Digital Object Identifier: 10.1214/aos/1024691473

Subjects:
Primary: 62H15 , 62H17

Keywords: Contingency tables , Fisher’s test , independence , likelihood ratio order , multivariate exponential family , Order restricted inference , peeling , stochastic order , Wilcoxon–Mann–Whitney test

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 6 • December 1998
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