Exact and approximate computation of the scatter halfspace depth

Xiaohui Liu (), Yuzi Liu (), Petra Laketa (), Stanislav Nagy () and Yuting Chen ()
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Xiaohui Liu: Jiangxi University of Finance and Economics
Yuzi Liu: Jiangxi University of Finance and Economics
Petra Laketa: Charles University
Stanislav Nagy: Charles University
Yuting Chen: University of Maryland

Computational Statistics, 2025, vol. 40, issue 1, No 21, 547-572

Abstract: Abstract 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 possible to define minimax optimal robust scatter estimators for multivariate data. The problem of exact computation of sHD for data of dimension $$d \ge 2$$ d ≥ 2 has, however, not been addressed in the literature. We develop an exact algorithm for the computation of sHD in any dimension d and implement it efficiently for any dimension $$d \ge 1$$ d ≥ 1 . Since the exact computation of sHD is slow especially for higher dimensions, we also propose two fast approximate algorithms. All our programs are freely available in the R package scatterdepth.

Keywords: Scatter halfspace depth; Depth; Exact computation; Approximate algorithm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01500-6

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