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

When applying a statistical method in practice it often occurs that some observations deviate
from the usual assumptions. However, many classical methods are sensitive to outliers. The …

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 …

Covariance matrix estimation is one of the most important problems in statistics. To
accommodate the complexity of modern datasets, it is desired to have estimation procedures …

Despite the absence of a natural ordering of Euclidean space for dimensions greater than
one, the effort to define vector‐valued quantile functions for multivariate distributions has …

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

Quantile Functions and Spread for Multivariate Distributions.-A New Definition of Multivariate
M-quantiles.-A Depth Function and a Scale Curve Based on Spatial Quantiles.-Sample …

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 …

The zonoid depth is useful in multivariate data analysis in order to describe an empirical
distribution by trimmed regions, so-called zonoid regions. The zonoid regions range from the …

Spatial quantiles, based on the L1 norm in a certain sense, provide an appealing vector
extension of univariate quantiles and generate a useful" volume" functional based on …