Spectral Analysis of Large Reflexive Generalized Inverse and Moore-Penrose Inverse Matrices

Taras Bodnar () and Nestor Parolya
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Taras Bodnar: Stockholm University, Department of Mathematics

Chapter Chapter 1 in Recent Developments in Multivariate and Random Matrix Analysis, 2020, pp 1-16 from Springer

Abstract: 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-56773-6_1

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DOI: 10.1007/978-3-030-56773-6_1

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