✦ LIBER ✦

Multivariate versions of Cochran theorems

✍ Scribed by Chi Song Wong; Hua Cheng; Joe Masaro

Book ID: 104156531
Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 430 KB
Volume: 291
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10239-2

No coin nor oath required. For personal study only.

✦ Synopsis

A general easily verifiable Cochran theorem is obtained for a normal random matrix Y with mean /' and covariance orr which may be singular and may not be or the form A 0-) ~, where l' is the population covariance: {y' JJ~Y};: )(with nonnegative definite H~.'s) is an independent family of Wishart lfj,(mi. E, I.,) random matrix yl H~-Y if and only if for IV =r;"-,1IV;, (W (/ J 1)2:'l' Of! ~_';I I) is of the form C (.) r witl: elf!C =Cand for all distinct i.] = 1. 2, ... , L. m, = I'(1V'-CIV t 11~), 1J~-1V 1 CW I 1I~=== 0 and i., = 1/rv; Ii ~:= , / H~!Q-l cw -/ ItjJt.

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