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...