The Annals of Probability

Majorization, Randomness and Dependence for Multivariate Distributions

Harry Joe

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Abstract

The preorder relation of Hardy, Littlewood and Polya (1929), Day (1973) and Chong (1974, 1976) is applied to multivariate probability densities. This preorder, which is called majorization here, can be interpreted as an ordering of randomness. When used to compare multivariate densities with the same marginal densities, it can be interpreted as an ordering of dependence or conditional dependence. Results in Hickey (1983, 1984) and Joe (1985) are generalized. A relative entropy function is proposed as a measure of dependence or conditional dependence for multivariate densities with the same marginals.

Article information

Source
Ann. Probab., Volume 15, Number 3 (1987), 1217-1225.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992093

Digital Object Identifier
doi:10.1214/aop/1176992093

Mathematical Reviews number (MathSciNet)
MR893926

Zentralblatt MATH identifier
0657.60022

JSTOR
links.jstor.org

Subjects
Primary: 62H20: Measures of association (correlation, canonical correlation, etc.)
Secondary: 62H99: None of the above, but in this section

Keywords
Majorization ordering of dependence entropy

Citation

Joe, Harry. Majorization, Randomness and Dependence for Multivariate Distributions. Ann. Probab. 15 (1987), no. 3, 1217--1225. doi:10.1214/aop/1176992093. https://projecteuclid.org/euclid.aop/1176992093


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