On Quadratic Forms of MultivariatetDistribution with Applications

Abstract

This note mainly aims to illustrate that some quadratic problems are robust in a sense with respect to the probabilistic distributions involved. The secondary moments of the quadratic forms of a multivariate t distribution are calculated. Then, the resulting formulae are applied to the quadratic problems of quadratic sufficiency and quadratic prediction. It is shown by revisiting the two problems that the same conclusions hold when the multivariate normal distribution is replaced with a multivariate t distribution.

A note on the consistency of the maximum likelihood estimator under multivariate linear cluster-weighted models

“…Furthermore, if ω > 2, then the covariance matrix of Z is equal to ω ω−2 Ξ (see, for example, Kots and Nadarajah, 2004). Finally, according to Rong et al (2012),…”