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.
Publié le : 1974-03-14
Classification:
Multivariate data,
complete two-way classification scheme,
multiple hypotheses,
Lawley-Hotelling statistics based on ranks,
joint distribution in small and large samples,
Berry-Esseen bounds,
62G10,
62H10,
60F05
@article{1176342665,
author = {Jensen, D. R.},
title = {On the Joint Distribution of Friedman's $\chi\_r^2$ Statistics},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 311-322},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342665}
}
Jensen, D. R. On the Joint Distribution of Friedman's $\chi_r^2$ Statistics. Ann. Statist., Tome 2 (1974) no. 1, pp. 311-322. http://gdmltest.u-ga.fr/item/1176342665/