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March, 1974 On the Joint Distribution of Friedman's $\chi_r^2$ Statistics
D. R. Jensen
Ann. Statist. 2(2): 311-322 (March, 1974). DOI: 10.1214/aos/1176342665


This study is concerned with the joint distribution of Gerig's (1969) statistics when applied to tests for shift in various marginal distributions pertaining to complete two-way multivariate data. The exact small-sample distribution can be found using conditional permutation arguments, and the limiting permutation distribution is shown to belong to a known class of multivariate chi-square distributions. A special case yields the limiting joint distribution of Friedman's (1937) $_{\chi r^2}$ statistics for the one-dimensional marginal distributions. Berry-Esseen bounds are given for the rate of convergence of the joint distribution to its limiting form when the underlying distributions are identical over replications.


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D. R. Jensen. "On the Joint Distribution of Friedman's $\chi_r^2$ Statistics." Ann. Statist. 2 (2) 311 - 322, March, 1974.


Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0275.62037
MathSciNet: MR397981
Digital Object Identifier: 10.1214/aos/1176342665

Primary: 62G10
Secondary: 60F05 , 62H10

Keywords: Berry-Esseen bounds , complete two-way classification scheme , joint distribution in small and large samples , Lawley-Hotelling statistics based on ranks , multiple hypotheses , multivariate data

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 2 • March, 1974
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