Abstract In 1975 John Tukey proposed a multivariate median which is the 'deepest'point in a
given data cloud in ℝ d. Later, in measuring the depth of an arbitrary point z with respect to …

An extensive update to a classic text Stochastic geometry and spatial statistics play a
fundamental role in many modern branches of physics, materials sciences, engineering …

A new procedure, called DD α-procedure, is developed to solve the problem of classifying d-
dimensional objects into q≥ 2 classes. The procedure is nonparametric; it uses q …

In recent years it has become popular to study machine learning problems in a setting of
ordinal distance information rather than numerical distance measurements. By ordinal …

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 …

Expectiles are the solution to an asymmetric least squares minimization problem for
univariate data. They resemble the quantiles, and just like them, expectiles are indexed by a …

A data depth measures the centrality of a point with respect to an empirical distribution.
Postulates are formulated, which a depth for functional data should satisfy, and a general …

The zero cell of a parametric class of random hyperplane tessellations depending on a
distance exponent and an intensity parameter is investigated, as the space dimension tends …

We suggest several constructions suitable to define the depth of set‐valued observations
with respect to a sample of convex sets or with respect to the distribution of a random closed …

Capacities are a common tool in decision making. Each capacity determines a core, which is
a polytope formed by additive measures. The problem of eliciting a single probability from …