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October 1997 Proof of the conjectures of H. Uhlig on the singular multivariate beta and the Jacobian of a certain matrix transformation
José A. Díaz-García, Ramón Gutiérrez Jáimez
Ann. Statist. 25(5): 2018-2023 (October 1997). DOI: 10.1214/aos/1069362383

Abstract

Uhlig proposes two conjectures. The first concerns the Jacobian of the transformation $Y = B \times B'$ where B is the matrix $m \times m$ and m and X, Y belong to the class of positive semidefinite matrices of the order of $m \times m$ of rank $n < m, S_{m,n^{\cdot}}^+$. The second is concerned with the singular multivariate Beta distribution. This article seeks to prove the two conjectures. The latter result is then extended to the case of the singular multivariate F distribution, and the respective density functions are located for the nonzero positive eigenvalues of the singular Beta and F matrices.

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José A. Díaz-García. Ramón Gutiérrez Jáimez. "Proof of the conjectures of H. Uhlig on the singular multivariate beta and the Jacobian of a certain matrix transformation." Ann. Statist. 25 (5) 2018 - 2023, October 1997. https://doi.org/10.1214/aos/1069362383

Information

Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0881.62058
MathSciNet: MR1474079
Digital Object Identifier: 10.1214/aos/1069362383

Subjects:
Primary: 62H10
Secondary: 62E15

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 1997
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