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Preliminary test estimation for multi-sample principal components

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  • Paindaveine, Davy
  • Rasoafaraniaina, Rondrotiana Joséa
  • Verdebout, Thomas

Abstract

Point estimation is considered in a multi-sample principal components setup, in a situation where it is suspected that the hypothesis of common principal components (CPC) holds. Preliminary test estimators of the various principal eigenvectors are proposed. Their asymptotic distributions are derived (i) under the CPC hypothesis, (ii) under sequences of hypotheses that are contiguous to the CPC hypothesis, and (iii) away from the CPC hypothesis. A Monte-Carlo study shows that the proposed estimators perform well, particularly so in the Gaussian case.

Suggested Citation

  • Paindaveine, Davy & Rasoafaraniaina, Rondrotiana Joséa & Verdebout, Thomas, 2017. "Preliminary test estimation for multi-sample principal components," Econometrics and Statistics, Elsevier, vol. 2(C), pages 106-116.
    • Handle: RePEc:eee:ecosta:v:2:y:2017:i:c:p:106-116
    DOI: 10.1016/j.ecosta.2017.01.004
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    References listed on IDEAS

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    1. Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2006. "General projection-pursuit estimators for the common principal components model: influence functions and Monte Carlo study," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 124-147, January.
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    4. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2014. "Efficient R-Estimation of Principal and Common Principal Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1071-1083, September.
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    6. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2011. "Optimal Rank-Based Tests for Common Principal Components," Working Papers ECARES ECARES 2011-032, ULB -- Universite Libre de Bruxelles.
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    8. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2010. "Testing for Common Principal Components under Heterokurticity," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 879-895.
    9. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2009. "Optimal rank-based testing for principal component," Working Papers ECARES 2009_013, ULB -- Universite Libre de Bruxelles.
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