Exact and approximate computation of the scatter halfspace depth

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-05-09 DOI:10.1007/s00180-024-01500-6

Xiaohui Liu, Yuzi Liu, Petra Laketa, Stanislav Nagy, Yuting Chen

引用次数: 0

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 \(d \ge 2\) 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 \(d \ge 1\). 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.

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散射半空间深度的精确和近似计算

散点半空间深度（sHD）是位置半空间深度（也称为 Tukey）的扩展，适用于散点的非参数分析。利用 sHD，可以定义多元数据的最小最优稳健散点估计值。然而，对于维数为 \(d \ge 2\) 的数据，sHD 的精确计算问题在文献中还没有得到解决。我们开发了一种在任意维度 d 下计算 sHD 的精确算法，并在任意维度（d\ge 1\ ）下有效地实现了这一算法。由于sHD的精确计算速度较慢，尤其是在高维情况下，因此我们还提出了两种快速近似算法。我们的所有程序都可以在R软件包scatterdepth中免费获取。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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