38 citations · 93 across the 17 of their papers we have counts for
19 papers
Resampling simplicial depth
Carsten Jentsch, Stanislav Nagy, Martin Wendler
The simplicial depth (SD) is a commonly used indicator of the centrality of points with respect to distributions on . Asymptotic theory for the…
Projection depth for functional data: Practical issues, computation and applications
Filip Bočinec, Stanislav Nagy, Hyemin Yeon
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure.…
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…
Projection depth for functional data: Theoretical properties
Filip Bočinec, Stanislav Nagy, Hyemin Yeon
We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projectio…
Which depth to use to construct functional boxplots?
Stanislav Nagy, Tomáš Mrkvička, Antonio Elías
This paper answers the question of which functional depth to use to construct a boxplot for functional data. It shows that integrated depths, e.g., the popular modified band depth,…
Robust Functional Regression with Discretely Sampled Predictors
Ioannis Kalogridis, Stanislav Nagy
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despi…
Another look at halfspace depth: Flag halfspaces with applications
Dušan Pokorný, Petra Laketa, Stanislav Nagy
The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of…
Exact and approximate computation of the scatter halfspace depth
Xiaohui Liu, Yuzi Liu, Petra Laketa +2
The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is…
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…
On exact computation of Tukey depth central regions
Vít Fojtík, Petra Laketa, Pavlo Mozharovskyi +1
The Tukey (or halfspace) depth extends nonparametric methods toward multivariate data. The multivariate analogues of the quantiles are the central regions of the Tukey depth, defin…
Integrated shape-sensitive functional metrics
Sami Helander, Petra Laketa, Pauliina Ilmonen +3
This paper develops a new integrated ball (pseudo)metric which provides an intermediary between a chosen starting (pseudo)metric d and the L_p distance in general function spaces.…
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…
Approximate computation of projection depths
Rainer Dyckerhoff, Pavlo Mozharovskyi, Stanislav Nagy
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minim…
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…
Scalar-on-function local linear regression and beyond
Frédéric Ferraty, Stanislav Nagy
Regressing a scalar response on a random function is nowadays a common situation. In the nonparametric setting, this paper paves the way for making the local linear regression base…
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…