Many quantitative measures of the degree of chirality or symmetry of a set have been
proposed in the literature. The main approaches from various areas are reviewed: chemistry …

A fairly general procedure is studied to perturb a multivariate density satisfying a weak form
of multivariate symmetry, and to generate a whole set of non-symmetric densities. The …

Statistical depth functions are being formulated ad hoc with increasing popularity in
nonparametric inference for multivariate data. Here we introduce several general structures …

Functional data are occurring more and more often in practice, and various statistical
techniques have been developed to analyze them. In this paper we consider multivariate …

A class of projection-based depth functions is introduced and studied. These projection-
based depth functions possess desirable properties of statistical depth functions and their …

A new multivariate concept of quantile, based on a directional version of Koenker and
Bassett's traditional regression quantiles, is introduced for multivariate location and multiple …

This book introduces a new representation of probability measures, the lift zonoid
representation, and demonstrates its usefulness in statistical applica tions. The material …

The main focus of this work is on providing a formal definition of statistical depth for
functional data on the basis of six properties, recognising topological features such as …

Statistical depth functions have become increasingly used in nonparametric inference for
multivariate data. Here the contours of such functions are studied. Structural properties of the …

Supplementary material: On a general definition of depth for functional data. The document
contains the proofs of all new theoretical results stated in this paper, detailed references to …