A new class of L_q-norm zonoid depths

2017/10/23 by Xiaohui Liu, Yuanyuan Li, Liu, Xiaohui +3
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.1710.08073

openalex publication_date 2017/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Zonoid depth, as a well-known ordering tool, has been widely used in multivariate analysis. However, since its depth value vanishes outside the convex hull of the data cloud, it suffers from the so-called `outside problem', which consequently hinders its many practical applications, e.g., classification. In this note, we propose a new class of L_q-norm zonoid depths, which has no such problem. Examples are also provided to illustrate their contours.

Citations

• Fast nonparametric classification based on data depth

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