Aiming at analysing multimodal or non-convexly supported distributionsthrough data depth, we introduce a local extension of depth. Our constructionis obtained by conditioning the distribution to appropriate depth-based neigh-borhoods, and has the advantages, among others, to maintain...

The minimum covariance determinant (MCD) estimator of scatter is one of the most famous robust procedures for multivariate scatter. Despite the quite important research activity related to this estimator, culminating in the recent thorough asymptotic study of Cator and Lopuhaä (2010, 2012), no...

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,...

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...

A new quantile regression concept, based on a directional version of Koenker and Bassett’s traditional single-output one, has been introduced in [Hallin, Paindaveine and ¡Siman, Annals of Statistics 2010, 635-703] for multiple-output regression problems. The polyhedral contours provided by...

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...