Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis
distance from the mean, which is based on the mean and the covariance matrix of the data …

Following the seminal idea of Tukey, data depth is a function that measures how close an
arbitrary point of the space is located to an implicitly defined center of a data cloud. Having …

Statistics is the science of extracting useful information from data, and a statistical model is
used to provide a useful approximation to some of the important characteristics of the …

The design of a metric between probability distributions is a longstanding problem motivated
by numerous applications in Machine Learning. Focusing on continuous probability …

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 …

Data depth is a concept in multivariate statistics that measures the centrality of a point in a
given data cloud in R d. If the depth of a point can be represented as the minimum of the …

Given data in R p, a Tukey κ-trimmed region is the set of all points that have at least Tukey
depth κ wrt the data. As they are visual, affine equivariant and robust, Tukey regions are …

A fast nonparametric procedure for classifying functional data is introduced. It consists of a
two-step transformation of the original data plus a classifier operating on a low-dimensional …

The computational complexity of some depths that satisfy the projection property, such as
the halfspace depth or the projection depth, is known to be high, especially for data of higher …

We study depth measures for multivariate data defined by integrating univariate depth
measures, specifically, integrated dual (ID) depth introduced by Cuevas and Fraiman (2009) …