On the Conditional Distribution of the Multivariate t Distribution

ABSTRACT

As alternatives to the normal distributions, t distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate t distribution are well documented in Kotz and Nadarajah's book, which, however, states a wrong conclusion about the conditional distribution of the multivariate t distribution. Previous literature has recognized that the conditional distribution of the multivariate t distribution also follows the multivariate t distribution. We provide an intuitive proof without directly manipulating the complicated density function of the multivariate t distribution.

Keywords:

• Bayes’ theorem
• Data augmentation
• Mahalanobis distance
• Normal mixture
• Representation

Acknowledgments

The author thanks the editor, associate editor, and three reviewers for their helpful comments.