Spectral analysis of large reflexive generalized inverse and Moore-Penrose inverse matrices
Statistics Theory
2023-04-19 v1 Probability
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2004.12932,
title = {Spectral analysis of large reflexive generalized inverse and Moore-Penrose inverse matrices},
author = {Taras Bodnar and Nestor Parolya},
journal= {arXiv preprint arXiv:2004.12932},
year = {2023}
}
Comments
13 pages, 1 figure, a letter/short article