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Multivariate versions of Bartlett’s formula

✍ Scribed by Nan Su; Robert Lund

Book ID
113726689
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
251 KB
Volume
105
Category
Article
ISSN
0047-259X

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A general easily checkable Cochran theorem is obtained for a normal random operator \(Y\). This result does not require that the covariance, \(\Sigma_{\mathbf{r}}\), of \(Y\) is nonsingular or is of the usual form \(A \otimes 2\); nor does it assume that the mean. \(\mu\). of \(Y\) is equal to zero.

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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