The Annals of Probability
- Ann. Probab.
- Volume 15, Number 3 (1987), 1217-1225.
Majorization, Randomness and Dependence for Multivariate Distributions
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.
Ann. Probab., Volume 15, Number 3 (1987), 1217-1225.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H20: Measures of association (correlation, canonical correlation, etc.)
Secondary: 62H99: None of the above, but in this section
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