Aiming at analyzing multimodal or nonconvexly supported distributions through data depth, we introduce a local extension of depth. Our construction is obtained by conditioning the distribution to appropriate depth-based neighborhoods and has the advantages, among others, of maintaining...

We propose rank-based estimators of principal components, both in the one-sample and, under the assumption of <italic>common principal components</italic>, in the <italic>m</italic>-sample cases. Those estimators are obtained via a rank-based version of Le Cam's one-step method, combined with an estimation of <italic>cross-information...</italic>