Singular random matrix decompositions: distributions

Authors:
José A. Díaz-García;Graciela González-Farías
Affiliations:
Dept. of Stats. and Comp., Universidad Autónoma Agraria Antonio Narro, Coahuila and Dept. of Prob. and Stats. of the Centro de Investigación en Matemáticas, Guanajuato, México;Department of Probability and Statistics, Centro de Investigación en Matemáticas, Callejón de Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, Guanajuato, México
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 3
Cited 4

The noncentral Bartlett decompositions and shape densities

Journal of Multivariate Analysis
Elliptically contoured models in statistics

Elliptically contoured models in statistics
Wishart and pseudo-Wishart distributions and some applications to shape theory

Journal of Multivariate Analysis

A note about measures and Jacobians of singular random matrices

Journal of Multivariate Analysis
Singular matrix variate beta distribution

Journal of Multivariate Analysis
Predictive inference for singular multivariate elliptically contoured distributions

Journal of Multivariate Analysis
Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions

Journal of Multivariate Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

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. 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.