Finite sample breakdown point of Tukey's halfspace median

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（5）
• 页码范围: 861-874
• 页数: 14页
• 语种: 英文
• DOI: 10.1007/s11425-016-0285-1

摘要

Tukey's halfspace median (HM),servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature.It is supposed and expected to preserve robustness property (the most outstanding property) of the univariate median.One of prevalent quantitative assessments of robustness is finite sample breakdown point (FSBP).Indeed,the FSBP of many multivariate medians have been identified,except for the most prevailing one—the Tukey's halfspace median.This paper presents a precise result on FSBP for Tukey's halfspace median.The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario,revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.