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>

type="main" xml:id="insr12047-abs-0001" <title type="main">Summary</title>One-sample and multi-sample tests on the concentration parameter of Fisher-von Mises-Langevin distributions on (hyper-)spheres have been well studied in the literature. However, only little is known about their behaviour under local alternatives,...

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step R-estimation method and investigate its asymptotic performances under...

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...

The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic...

Very general concepts of scatter, extending the traditional notion of covariance matrices, have become classical tools in robust multivariate analysis. In many problems of practical importance (principal components, canonical correlation, testing for sphericity), only homogeneous functions of...

Chernoff and Savage [Asymptotic normality and efficiency of certain non-parametric tests, Ann. Math. Statist. 29 (1958) 972-994] established that, in the context of univariate location models, Gaussian-score rank-based procedures uniformly dominate--in terms of Pitman asymptotic relative...

In recent years, the skew-normal models introduced by Azzalini (1985) [1]-and their multivariate generalizations from Azzalini and Dalla Valle (1996) [4]-have enjoyed an amazing success, although an important literature has reported that they exhibit, in the vicinity of symmetry, singular Fisher...