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Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies

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  • Croux, C.
  • Haesbroeck, G.
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    Abstract

    A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper the authors derive the influence functions and the corresponding asumptotic variances for these robust estimators of eigenvalues and eigenvectors. The behavior of several of these estimators is investigated by a simulation study. Finally, the use of empirical influence functions id illustrated by a real data example.

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    Bibliographic Info

    Paper provided by UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie in its series Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie with number 9908.

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    Length: 26 pages
    Date of creation: 1999
    Date of revision:
    Handle: RePEc:fth:gemame:9908

    Contact details of provider:
    Postal: UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie. 4000 Liege, BELGIQUE
    Web page: http://www.quantom.hec.ulg.ac.be/
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    Keywords: ESTIMATOR ; MATHEMATICAL ANALYSIS ; ECONOMETRICS;

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    Cited by:
    1. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 1-73, June.

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