Spectral analysis of large reflexive generalized inverse and Moore-Penrose inverse matrices
arXiv:2004.12932 · doi:10.1007/978-3-030-56773-6_1
Abstract
A reflexive generalized inverse and the Moore-Penrose inverse are often confused in statistical literature but in fact they have completely different behaviour in case the population covariance matrix is not a multiple of identity. In this paper, we study the spectral properties of a reflexive generalized inverse and of the Moore-Penrose inverse of the sample covariance matrix. The obtained results are used to assess the difference in the asymptotic behaviour of their eigenvalues.
13 pages, 1 figure, a letter/short article