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...

This paper sheds some new light on the multivariate (projectional) quantiles recently introduced in Kong and Mizera (2008). Contrary to the sophisticated set analysis used there, we adopt a more parametric approach and study the subgradient conditions associated with these quantiles. In this...