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

Bodnar, T.; Parolya, N.

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

Book chapter (2020)

Authors

T. Bodnar Stockholm University

N. Parolya Statistics -

Research Group

Statistics () (TU Delft)

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Published Date

2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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.

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