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 …

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 …

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 …

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 …

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 …

Depth notions in location have generated tremendous attention in the literature. In fact, data
depth and its applications remain as one of the most active research topics in statistics over …

Because it determines a center-outward ordering of observations in $\mathbb {R}^ d $ with $
d\geq 2$, the concept of statistical depth permits to define quantiles and ranks for …

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 …

Simulated annealing is a widely used algorithm for the computation of global optimization
problems in computational chemistry and industrial engineering. However, global optimum …

Because it determines a center-outward ordering of observations in R d with d≥ 2, the
concept of statistical depth permits to define quantiles and ranks for multivariate data and …