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

R. Dennis Cook, Liliana Forzani

Research output: Contribution to journalArticle

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)146-158
Number of pages13
JournalElectronic Journal of Statistics
StatePublished - Aug 5 2011



  • Inverse wishart distribution
  • Moore-penrose generalized inverse
  • Singular inversewishart distributions
  • Tensor functions

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