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Exact and approximate computation of the scatter halfspace depth

Author

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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)

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.

Suggested Citation

  • Xiaohui Liu & Yuzi Liu & Petra Laketa & Stanislav Nagy & Yuting Chen, 2025. "Exact and approximate computation of the scatter halfspace depth," Computational Statistics, Springer, vol. 40(1), pages 547-572, January.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01500-6
    DOI: 10.1007/s00180-024-01500-6
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    References listed on IDEAS

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    1. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    2. Dyckerhoff, Rainer & Mozharovskyi, Pavlo & Nagy, Stanislav, 2021. "Approximate computation of projection depths," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    3. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
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