The study of orderings for positive dependence on bivariate empirical distributions can be viewed as the study of partial orderings on the set $S_N$ of all permutations of the integers $1,\ldots,N$. This paper extends earlier bivariate results to multivariate empirical distributions, with focus on the trivariate case. In terms of a newly defined notion of relative rearrangement, characterizations are given of the more positively upper orthant dependent ordering and related orderings. A new partial ordering describing concordance on $(S_N)^m$ is also introduced and connected with the positively upper orthant dependence ordering.
Publié le : 1993-11-14
Classification:
Permutation,
partial ordering,
ordering for positive dependence,
more concordant,
more PUOD,
empirical rank distribution,
relative rearrangement,
arrangement increasing function,
62H05,
20B99
@article{1177005281,
author = {Metry, Magdy H. and Sampson, Allan R.},
title = {Orderings for Positive Dependence on Multivariate Empirical Distributions},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 1241-1251},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005281}
}
Metry, Magdy H.; Sampson, Allan R. Orderings for Positive Dependence on Multivariate Empirical Distributions. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 1241-1251. http://gdmltest.u-ga.fr/item/1177005281/