Efficient R-Estimation of Principal and Common Principal Components
We propose rank-based estimators of principal components, both in the one-sample and, under the assumption of common principal components , in the m -sample cases. Those estimators are obtained via a rank-based version of Le Cam's one-step method, combined with an estimation of cross-information quantities . Under arbitrary elliptical distributions with, in the m -sample case, possibly heterogeneous radial densities, those R-estimators remain root- n consistent and asymptotically normal, while achieving asymptotic efficiency under correctly specified radial densities. Contrary to their traditional counterparts computed from empirical covariances, they do not require any moment conditions. When based on Gaussian score functions, in the one-sample case, they uniformly dominate their classical competitors in the Pitman sense. Their AREs with respect to other robust procedures are quite high-up to 30, in the Gaussian case, with respect to minimum covariance determinant estimators. Their finite-sample performances are investigated via a Monte Carlo study.
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|Date of creation:||Apr 2013|
|Publication status:||Published by:|
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- 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.
- Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
- Graciela Boente, 2002. "Influence functions and outlier detection under the common principal components model: A robust approach," Biometrika, Biometrika Trust, vol. 89(4), pages 861-875, December.
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