We consider asymptotic inference for the concentration of directional data. More precisely, wepropose tests for concentration (i) in the low-dimensional case where the sample size n goes to infinity andthe dimension p remains fixed, and (ii) in the high-dimensional case where both n and p become...

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>