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 article defines and studies a depth for multivariate functional data. By the multivariate
nature and by including a weight function, it acknowledges important characteristics of …

For computing the exact value of the halfspace depth of a point wrt a data cloud of n points in
arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole …

A proper fusion of complex data is of interest to many researchers in diverse fields, including
computational statistics, computational geometry, bioinformatics, machine learning, pattern …

The linear least trimmed squares (LTS) estimator is a statistical technique for fitting a linear
model to a set of points. Given a set of n points in ℝ d and given an integer trimming …

In this paper, ridge and non-ridge type estimators and their robust forms are defined in the
semiparametric regression model when the errors are dependent and some non-stochastic …

Halfspace depth (HD), aka Tukey depth, is one of the most prevailing depth notions among
all its competitors. To exactly compute the HD in R d (d> 2) is a challenging task …

A Monte Carlo approximation algorithm for the Tukey depth problem in high dimensions is
introduced. The algorithm is a generalization of an algorithm presented by Rousseeuw and …

Tukey's depth (or halfspace depth) is a widely used measure of centrality for multivariate
data. However, exact computation of Tukey's depth is known to be a hard problem in high …

As statistical data sets grow larger and larger, the availability of fast and efficient algorithms
becomes ever more important in practice. Classical methods are often easy to compute …