Search

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.

Assuming that the random matrix X has a singular or non-singular matrix variate elliptically contoured distribution, the density function of the Moore–Penrose inverse Z = ( X ′ X ) + is given with respect to the Hausdorff measure. The result is applied to Bayesian inference for a general multivariate linear regression model with matrix variate elliptically distributed errors. Some results concerning the posterior joint and marginal distributions of the parameters are obtained.