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Singular random matrix decompositions: distributions

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  • Díaz García, José A.
  • González Farías, Graciela

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. 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.

Suggested Citation

  • Díaz García, José A. & González Farías, Graciela, 2002. "Singular random matrix decompositions: distributions," DES - Working Papers. Statistics and Econometrics. WS ws024211, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws024211
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    References listed on IDEAS

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    1. Díaz-García, José A. & Jáimez, Ramón Gutierrez & Mardia, Kanti V., 1997. "Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 73-87, October.
    2. Goodall, Colin & Mardia, Kanti V., 1992. "The noncentral Bartlett decompositions and shape densities," Journal of Multivariate Analysis, Elsevier, vol. 40(1), pages 94-108, January.
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