| Title | Range of correlation matrices for dependent random variables with given marginal distributions |
| Publication Type | Conference Paper |
| Year of Publication | 2006 |
| Authors | Joe, H |
| Editor | Balakrishnan, N, Castillo, E, Sarabia, JM |
| Conference Name | Advances in Distribution Theory, Order Statistics, and Inference |
| Publisher | Birkhauser Boston |
| ISBN Number | 0-8176-4361-3 |
| Keywords | Copula, elliptically contoured, Frechet bounds, Partial correlation, spherically symmetric |
| 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. |
| DOI | 10.1007/0-8176-4487-3_8 |
