Pseudo-inverse multivariate/matrix-variate distributions

Zhihua Zhang

Journal of Multivariate Analysis, 2007, vol. 98, issue 8, 1684-1692

Abstract: The Moore-Penrose inverse of a singular or nonsquare matrix is not only existent but also unique. In this paper, we derive the Jacobian of the transformation from such a matrix to the transpose of its Moore-Penrose inverse. Using this Jacobian, we investigate the distribution of the Moore-Penrose inverse of a random matrix and propose the notion of pseudo-inverse multivariate/matrix-variate distributions. For arbitrary multivariate or matrix-variate distributions, we can develop the corresponding pseudo-inverse distributions. In particular, we present pseudo-inverse multivariate normal distributions, pseudo-inverse Dirichlet distributions, pseudo-inverse matrix-variate normal distributions and pseudo-inverse Wishart distributions.

Keywords: Matrix-variate; distribution; The; Moore-Penrose; generalized; inverse; Pseudo-inverse; multivariate; distribution; Pseudo-inverse; matrix-variate; distribution (search for similar items in EconPapers)
Date: 2007
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