Range of correlation matrices for dependent random variables with given marginal distributions

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Range of correlation matrices for dependent random variables with given marginal distributions

TitleRange of correlation matrices for dependent random variables with given marginal distributions
Publication TypeConference Paper
Year of Publication2006
AuthorsJoe, H
EditorBalakrishnan, N, Castillo, E, Sarabia, JM
Conference NameAdvances in Distribution Theory, Order Statistics, and Inference
PublisherBirkhauser Boston
ISBN Number0-8176-4361-3
KeywordsCopula, elliptically contoured, Frechet bounds, Partial correlation, spherically symmetric
AbstractLet 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.
DOI10.1007/0-8176-4487-3_8