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Singular random matrix decompositions: distributions

Listed author(s):
  • González Farías, Graciela
  • Díaz García, José A.
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    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.

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    Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws024211.

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    Date of creation: Sep 2002
    Handle: RePEc:cte:wsrepe:ws024211
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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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