A better approximation of moments of the eigenvalues and eigenvectors of the sample covariance matrix

A. Enguix-González, J.L. Moreno-Rebollo and J.M. Muñoz-Pichardo

Journal of Multivariate Analysis, 2015, vol. 142, issue C, 133-143

Abstract: Lawley (Lawley, 1956) obtained an approximation, through the first terms of a series expansion, of certain moments of an eigenvalue of the sample covariance matrix. The aim of this paper is to improve that approximation and to calculate a similar approximation for certain moments of the associated eigenvector. The results have practical applications in certain fields of Statistics, such as Influence Analysis.

Keywords: Eigenvalues; Eigenvectors; Sample covariance matrix; Principal Component Analysis; Influence Analysis (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.jmva.2015.08.002

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