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- Article] USE OF NONNULL MODELS FOR RANK STATISTICS IN BIVARIATE, 2-SAMPLE, AND ANALYSIS OF VARIANCE PROBLEMS
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DocNo of ILP: 8539
Doc. Type: Article
Title: USE OF NONNULL MODELS FOR RANK STATISTICS IN BIVARIATE, 2-SAMPLE, AND ANALYSIS OF VARIANCE PROBLEMS
Authors: CHUNG, L; MARDEN, JI
Full Name of Authors: CHUNG, L; MARDEN, JI
Keywords by Author: DISCORDANT PAIRS; EXPONENTIAL FAMILY; KENDALL TAU; PERMUTATIONS
Keywords Plus:
Abstract: A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair of vectors of length n, where both are permutations of the first n integers or one is a fixed and arbitrary design vector and the other a permutation. The model is Mallow's phi-model, a one-parameter exponential family with natural statistic the number of discordant pairs between the two vectors. This model originated with Mann and has appeared in many articles since. We extend the model to cases in which there may be ties in the observations and to analysis of variance problems (in which there are several parameters). The first four sections describe the models and verify the asymptotic normality of the statistics and the maximum likelihood estimators of the parameters, as well as the asymptotic chi-squared nature of the likelihood ratio statistics under the null hypotheses. In Section 5 we compare the model to some other typical models. Section 6 contains examples, including analysis of the 1970 Draft Lottery data, and a 2 x 2 x 2 analysis of variance design.
Cate of OECD: Mathematics
Year of Publication: 1991
Business Area: lottery
Detail Business: lottery
Country: USA
Study Area:
Name of Journal: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Language: English
Country of Authors: UNIV ILLINOIS,DEPT STAT,CHAMPAIGN,IL 61820
Press Adress: CHUNG, L (reprint author), ABBOTT LABS,CLIN STAT,N CHICAGO,IL 60064, USA.
Email Address:
Citaion:
Funding:
Lists of Citation: BARTON DE, 1958, BIOMETRIKA, V45, P166, DOI 10.2307/2333054; CRITCHLOW D, 1986, 8615 PURD U DEP STAT; Critchlow D, 1985, METRIC METHODS ANAL; DIACONIS P, 1988, I MATH STATISTICS LE; FEIGIN PD, 1978, J R STAT SOC B, V40, P203; FIENBERG SE, 1971, SCIENCE, V171, P255, DOI 10.1126/science.171.3968.255; FLIGNER MA, 1986, J ROY STAT SOC B MET, V48, P359; FLIGNER MA, 1988, J AM STAT ASSOC, V83, P892, DOI 10.2307/2289322; Gibbons JD, 1985, NONPARAMETRIC STATIS; Kendall MG, 1975, RANK CORRELATION MET; Lehmann E. L., 1983, THEORY POINT ESTIMAT; MALLOWS CL, 1957, BIOMETRIKA, V44, P114, DOI 10.2307/2333244; Mann HB, 1945, ECONOMETRICA, V13, P245, DOI 10.2307/1907187; SCHULMAN RS, 1979, PSYCHOMETRIKA, V44, P3, DOI 10.1007/BF02293781; SHIRLEY EAC, 1987, APPL STAT-J ROY ST C, V36, P205, DOI 10.2307/2347552; SILVERBERG AR, 1980, THESIS PRINCETON U; THOMPSON GL, 1990, NOTE RANK TRANSFORM
Number of Citaion: 17
Publication: AMER STATIST ASSN
City of Publication: ALEXANDRIA
Address of Publication: 1429 DUKE ST, ALEXANDRIA, VA 22314
ISSN: 0162-1459
29-Character Source Abbreviation: J AM STAT ASSOC
ISO Source Abbreviation: J. Am. Stat. Assoc.
Volume: 86
Version: 413
Start of File: 188
End of File: 200
DOI: 10.2307/2289730
Number of Pages: 13
Web of Science Category: Statistics & Probability
Subject Category: Mathematics
Document Delivery Number: FD712
Unique Article Identifier: WOS:A1991FD71200025
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