In article <[EMAIL PROTECTED]>, Ralph Lorentzen <[EMAIL PROTECTED]> wrote: >I'm new to this group, so my question may have been answered earlier.
>Suppose we know all marginal distributions of n random variables. >There are of >course in general many joint distributions which have these marginal >distributions, (We may for instance multiply the marginal >distributions if we assume independence.) I want to narrow down the >choice by specifying all >covariances. It is easy to see that I cannot choose any set of >covariances even if I secure that the variance/covariance matrix to be >positive semidefinite. Is there a set of conditions on the covariances >which guarantees that a joint distribution exists? Other than independence, no. For two random variables, one can obtain the maximum and minimum covariance for the pair fairly easily. Of course, the set of covariance matrices for which a joint distribution exists must be convex. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
