2021/12/15 by Yiyuan She, She, Yiyuan, Shao Tang +3
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.2112.08475
openalex publication_date 2021/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tukey's depth offers a powerful tool for nonparametric inference and estimation, but also encounters serious computational and methodological difficulties in modern statistical data analysis. This paper studies how to generalize and compute Tukey-type depths in multi-dimensions. A general framework of influence-driven polished subspace depth, which emphasizes the importance of the underlying influence space and discrepancy measure, is introduced. The new matrix formulation enables us to utilize state-of-the-art optimization techniques to develop scalable algorithms with implementation ease and guaranteed fast convergence. In particular, half-space depth as well as regression depth can now be computed much faster than previously possible, with the support from extensive experiments. A companion paper is also offered to the reader in the same issue of this journal.