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'sone-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 e ciency under correctly speci ed densities. Contrary to their traditional counterparts computed from empirical covariances, they do not require any moment conditions. When based on Gaussian scorefunctions, in the one-sample case, they moreover uniformly dominate their classical competitors in the Pitman sense. Their finite-sample performances are investigatedvia a Monte-Carlo study.
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