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This paragraph replaces a previous subsection in the article "Multivariate t-distribution".
Conditional Distribution
editThis was demonstrated by Muirhead [1] though previously derived using the simpler ratio representation above, by Cornish.[2] Let vector follow the multivariate t distribution and partition into two subvectors of elements:
where , the known mean vector is and the scale matrix is .
Then
explicitly
where
- is the conditional mean
- is the Schur complement of
- is the squared Mahalanobis distance of from with scale matrix
- ^ Muirhead, Robb (1982). Aspects of Multivariate Statistical Theory. USA: Wiley. pp. 32–36 Theorem 1.5.4. ISBN 978-0-47 1-76985-9.
- ^ Cornish, E A (1954). "The Multivariate t-Distribution Associated with a Set of Normal Sample Deviates". Australian Journal of Physics. 7: 531–542. doi:10.1071/PH550193.