@conference { ISI:000238122900008,
title = {Range of correlation matrices for dependent random variables with given marginal distributions},
booktitle = {Advances in Distribution Theory, Order Statistics, and Inference},
series = {Statistics for Industry and Technology},
year = {2006},
note = {International Conference on Distribution Theory, Order Statistics, and Inference, Univ Cantabria, Santander, SPAIN, JUN 16-18, 2004},
pages = {125-142},
publisher = {Birkhauser Boston},
organization = {Birkhauser Boston},
type = {Proceedings Paper},
abstract = {Let X-1, center dot center dot center dot, X-d be d (d >= 3) dependent random variables with finite variances such that X-j similar to F-j. Results on the set S-d(F-1, center dot center dot center dot, F-d) of possible correlation matrices with given margins are obtained; this set is relevant for simulating dependent random variables with given marginal distributions and a given correlation matrix. When F-1 = (...) = F-d = F, we let S-d(F) denote the set of possible correlation matrices. Of interest is the set of F for which Sd(F) is the same as the set of all non-negative definite correlation matrices; using a construction with conditional distributions, we show that this property holds only if F is a (location-scale shift of a) margin of a (d-1)-dimensional spherical distribution.},
keywords = {Copula, elliptically contoured, Frechet bounds, Partial correlation, spherically symmetric},
isbn = {0-8176-4361-3},
doi = {10.1007/0-8176-4487-3_8},
author = {Joe, Harry},
editor = {Balakrishnan, N and Castillo, E and Sarabia, J. M.}
}