On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix

Abstract

The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. The article complements the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart matrix are close to the degrees of freedom of the distribution.

Keywords

Expectation and dispersion matrix; Moore-Penrose inverse; Wishart matrix

Published in

Electronic Journal Of Linear Algebra
2020, volume: 36, pages: 124-133
Publisher: INT LINEAR ALGEBRA SOC

SLU Authors

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    
  • Linköping University

UKÄ Subject classification

Discrete Mathematics

Publication identifier

• DOI: https://doi.org/10.13001/ela.2020.5091

Permanent link to this page (URI)

https://res.slu.se/id/publ/105426