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December 2010 Optimal rank-based testing for principal components
Marc Hallin, Davy Paindaveine, Thomas Verdebout
Ann. Statist. 38(6): 3245-3299 (December 2010). DOI: 10.1214/10-AOS810


This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Davis (1977) and Tyler (1981, 1983). The rank-based tests address a much broader class of problems, where covariance matrices need not exist and principal components are associated with more general scatter matrices. The proposed tests are shown to outperform daily practice both from the point of view of validity as from the point of view of efficiency. This is achieved by utilizing the Le Cam theory of locally asymptotically normal experiments, in the nonstandard context, however, of a curved parametrization. The results we derive for curved experiments are of independent interest, and likely to apply in other contexts.


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Marc Hallin. Davy Paindaveine. Thomas Verdebout. "Optimal rank-based testing for principal components." Ann. Statist. 38 (6) 3245 - 3299, December 2010.


Published: December 2010
First available in Project Euclid: 20 September 2010

zbMATH: 1373.62295
MathSciNet: MR2766852
Digital Object Identifier: 10.1214/10-AOS810

Primary: 62H25
Secondary: 62G35

Keywords: curved experiments , Elliptical densities , local asymptotic normality , multivariate ranks and signs , principal components , scatter matrix , shape matrix , tests for eigenvalues , tests for eigenvectors

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 6 • December 2010
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