Singular random matrix decompositions: distributions |
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Authors: | José A. Dí az-Garcí a,Graciela Gonzá lez-Farí as |
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Affiliation: | a Department of Statistics and Computation, Universidad Autónoma Agraria Antonio Narro, 25315 Buenavista, Saltillo, Coahuila, México b Department of Probability and Statistics, Centro de Investigación en Matemáticas, Callejón de Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, Guanajuato, México |
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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. |
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Keywords: | 62E15 60E05 |
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