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November, 1993 Orderings for Positive Dependence on Multivariate Empirical Distributions
Magdy H. Metry, Allan R. Sampson
Ann. Appl. Probab. 3(4): 1241-1251 (November, 1993). DOI: 10.1214/aoap/1177005281


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.


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Magdy H. Metry. Allan R. Sampson. "Orderings for Positive Dependence on Multivariate Empirical Distributions." Ann. Appl. Probab. 3 (4) 1241 - 1251, November, 1993.


Published: November, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0795.62051
MathSciNet: MR1241043
Digital Object Identifier: 10.1214/aoap/1177005281

Primary: 62H05
Secondary: 20B99

Keywords: arrangement increasing function , empirical rank distribution , more concordant , more PUOD , ordering for positive dependence , partial ordering , permutation , relative rearrangement

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 4 • November, 1993
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