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...

This paper provides optimal testing procedures for the m-sample null hypothesis of Common Principal Components (CPC) under possibly non Gaussian and heterogenous elliptical densities. We first establish, under very mild assumptions that do not require finite moments of order four, the local...

As a reaction to the restrictive Gaussian assumptions that are usually part of graphical models, Vogel and Fried [17] recently introduced elliptical graphical models, in which the vector of variables at hand is assumed to have an elliptical distribution. The present work introduces a class of...

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 Tyler (1981,...

We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical linear multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests,...

One-sample and multi-sample tests on the concentration parameter of Fisher-vonMises-Langevin (FvML) distributions have been well studied in the literature. However,only very little is known about their behavior under local alternatives, whichis due to complications inherent to the curved nature...