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Conditional independence between two variables given any conditioning subset implies block diagonal covariance matrix for multivariate Gaussian distributions

Let be a multivariate Gaussian variable with covariance matrix [Sigma]. For i and j in , we show that if the conditional covariance between xi and xj given any conditioning set is equal to zero, then [Sigma] is block diagonal and i and j belong to two different blocks.
Year of publication:
2008
Authors: Marrelec, Guillaume ; Benali, Habib
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 78.2008, 13, p. 1922-1928
Publisher: Elsevier
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10005223905
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