38 citations · 93 across the 17 of their papers we have counts for
8 papers · 1 filter
Estimating axial symmetry using random projections
Alejandro Cholaquidis, Ricardo Fraiman, Manuel Hernández-Banadik +1
We study the directions of axial symmetry of multivariate distributions and relate the measure or cardinality of this set to spherical symmetry. Under Carleman's condition, two ind…
Partial reconstruction of measures from halfspace depth
Petra Laketa, Stanislav Nagy
The halfspace depth of a -dimensional point with respect to a finite (or probability) Borel measure in is defined as the infimum of the -masses of all…
Halfspace depth for general measures: The ray basis theorem and its consequences
Petra Laketa, Stanislav Nagy
The halfspace depth is a prominent tool of nonparametric multivariate analysis. The upper level sets of the depth, termed the trimmed regions of a measure, serve as a natural gener…
Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis
George Wynne, Stanislav Nagy
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data livin…
Uniform convergence rates for the approximated halfspace and projection depth
Stanislav Nagy, Rainer Dyckerhoff, Pavlo Mozharovskyi
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 h…
Illumination depth
Stanislav Nagy, Jiří Dvořák
The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resoluti…
Halfspace depth does not characterize probability distributions
Stanislav Nagy
We give examples of different multivariate probability distributions whose halfspace depths coincide at all points of the sample space.
Data depth and floating body
Stanislav Nagy, Carsten Schuett, Elisabeth M. Werner
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Halfspace depth may be regarde…