Functions of singular random matrices with applications |
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Authors: | José A. Díaz-García Ramón Gutiérrez-Jáimez |
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Affiliation: | (1) Department of Statistics and Computation, Universidad Autónoma Agraria Antonio Narro, 25315 Buenavista, Saltillo, COAHUILA, México;(2) Department of Statistics and Operations Research, University of Granada, Spain |
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Abstract: | This article describes how the Jacobian is found for certain functions of a singular random matrix, both in the general case and in that of a non-negative, definite random matrix. The Jacobian of the transformationV=S 2 is found whenS is non-negative definite; in addition, the Jacobian of the transformationY=X + is determined whenX + is the generalized, or Moore-Penrose, inverse ofX. Expressions for the densities of the generalized inverse of the central beta and F singular random matrices are proposed. Finally, two applications in the field of Bayesian inference are presented. This work was supported in part by the research project 39017E of CONACYT-México This article was written during the first author's stay as a Visiting Professor in the Department of Statistics at the University of Granada, Spain |
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Keywords: | Matrix-variate inverse beta and F distributions Jacobian, Hausdorff measure inverse singular distribution inverse Wishart and pseudo-Wishart singular distributions Bayesian inference |
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