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

Guillaume Marrelec and Habib Benali

Statistics & Probability Letters, 2008, vol. 78, issue 13, 1922-1928

Abstract: 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.

Date: 2008
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