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December, 1990 Partial Orders on Permutations and Dependence Orderings on Bivariate Empirical Distributions
H. W. Block, D. Chhetry, Z. Fang, A. R. Sampson
Ann. Statist. 18(4): 1840-1850 (December, 1990). DOI: 10.1214/aos/1176347882

Abstract

Three well-known partial orderings and one new one, designated by $\geq_{b_t}, t = 1, 2, 3, 4$, are defined on permutations of $\{1, 2, \cdots, n\}$ through a unified approach. Various formulations of these partial orderings are also considered. With the aid of these formulations we show that the four orderings on permutations are equivalent to positive dependence orderings defined over empirical distributions based on rank data. In particular, we show that the orderings $b_1, b_2, b_3$ and $b_4$ are equivalent, respectively, to more concordant, more row regression dependent, more column regression dependent and more associated.

Citation

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H. W. Block. D. Chhetry. Z. Fang. A. R. Sampson. "Partial Orders on Permutations and Dependence Orderings on Bivariate Empirical Distributions." Ann. Statist. 18 (4) 1840 - 1850, December, 1990. https://doi.org/10.1214/aos/1176347882

Information

Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0714.62046
MathSciNet: MR1074439
Digital Object Identifier: 10.1214/aos/1176347882

Subjects:
Primary: 62H05
Secondary: 20B99

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 4 • December, 1990
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