Exactly computing bivariate projection depth contours and median

2011/12/28 by Xiaohui Liu, Liu, Xiaohui, Yijun Zuo +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #62F10 #62F35 #62F40 #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Computation (stat.CO) #FOS: Computer and information sciences #Image and Object Detection Techniques

paper · pdf · doi:10.48550/arxiv.1112.6162

openalex publication_date 2011/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Among their competitors, projection depth and its induced estimators are very favorable because they can enjoy very high breakdown point robustness without having to pay the price of low efficiency, meanwhile providing a promising center-outward ordering of multi-dimensional data. However, their further applications have been severely hindered due to their computational challenge in practice. In this paper, we derive a simple form of the projection depth function, when (μ, σ) = (Med, MAD). This simple form enables us to extend the existing result of point-wise exact computation of projection depth (PD) of Zuo and Lai (2011) to depth contours and median for bivariate data.

Citations

• The quickhull algorithm for convex hulls

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