Economics at your fingertips  

Testing for Common Principal Components under Heterokurticity

Marc Hallin (), Davy Paindaveine and Thomas Verdebout

Journal of Nonparametric Statistics, 2010, vol. 22, issue 7, 879-895

Abstract: The so-called common principal components (CPC) model, in which the covariance matrices Σi of m populations are assumed to have identical eigenvectors, was introduced by Flury [Flury, B. (1984), ‘Common Principal Components in k Groups’, Journal of the American Statistical Association, 79, 892–898]. Gaussian parametric inference methods [Gaussian maximum-likelihood estimation and Gaussian likelihood ratio test (LRT)] have been fully developed for this model, but their validity does not extend beyond the case of elliptical densities with common Gaussian kurtosis. A non-Gaussian (but still homokurtic) extension of Flury's Gaussian LRT for the hypothesis of CPC [Flury, B. (1984), ‘Common Principal Components in k Groups’, Journal of the American Statistical Association, 79, 892–898] is proposed in Boik [Boik, J.R. (2002), ‘Spectral Models for Covariance Matrices’, Biometrika, 89, 159–182], see also Boente and Orellana [Boente, G., and Orellana, L. (2001), ‘A Robust Approach to Common Principal Components’, in Statistics in Genetics and in the Environmental Sciences, eds. Sciences Fernholz, S. Morgenthaler, and W. Stahel, Basel: Birkhauser, pp. 117–147] and Boente, Pires and Rodrigues [Boente, G., Pires, A.M., and Rodrigues I.M. (2009), ‘Robust Tests for the Common Principal Components Model’, Journal of Statistical Planning and Inference, 139, 1332–1347] for robust versions. In this paper, we show how Flury's LRT can be modified into a pseudo-Gaussian test which remains valid under arbitrary, hence possibly heterokurtic, elliptical densities with finite fourth-order moments, while retaining its optimality features at the Gaussian.

Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed

Downloads: (external link) (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().

Page updated 2019-06-08
Handle: RePEc:taf:gnstxx:v:22:y:2010:i:7:p:879-895