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

Book Chapter (2020)
Author(s)

Taras Bodnar (Stockholm University)

N. Parolya (TU Delft - Statistics)

DOI related publication
https://doi.org/10.1007/978-3-030-56773-6_1 Final published version
More Info
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Publication Year
2020
Language
English
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Pages (from-to)
1-16
Publisher
Springer
ISBN (print)
978-3-030-56772-9
ISBN (electronic)
978-3-030-56773-6
Downloads counter
146
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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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