Electronic Journal of Statistics

On the mean and variance of the generalized inverse of a singular Wishart matrix

R. Dennis Cook and Liliana Forzani

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We derive the first and the second moments of the Moore-Penrose generalized inverse of a singular standard Wishart matrix without relying on a density. Instead, we use the moments of an inverse Wishart distribution and an invariance argument which is related to the literature on tensor functions. We also find the order of the spectral norm of the generalized inverse of a Wishart matrix as its dimension and degrees of freedom diverge.

Article information

Electron. J. Statist., Volume 5 (2011), 146-158.

First available in Project Euclid: 15 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H05: Characterization and structure theory
Secondary: 62E15: Exact distribution theory

Inverse Wishart distribution Moore-Penrose generalized inverse singular inverse Wishart distributions tensor functions


Cook, R. Dennis; Forzani, Liliana. On the mean and variance of the generalized inverse of a singular Wishart matrix. Electron. J. Statist. 5 (2011), 146--158. doi:10.1214/11-EJS602. https://projecteuclid.org/euclid.ejs/1300198786

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