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math.ST2024
Theoretical properties of angular halfspace depth
Stanislav Nagy, Petra Laketa
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonpar…
math.ST2022
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…
math.ST2021★ 8 cited
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…