BREAKDOWN PROPERTIES OF LOCATION ESTIMATES BASED ON HALF-SPACE DEPTH AND PROJECTED OUTLYINGNESS

• 成果类型: Article
• 署名作者: DONOHO, DL; GASKO, M
• 署名单位: University of California System; University of California Berkeley; California State University System; San Jose State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348890
• 发表日期: 1992
• 页码: 1803-1827
• 关键词: multivariate location; squares regression; matrices; PURSUIT; point

摘要

We describe multivariate generalizations of the median, trimmed mean and W estimates. The estimates are based on a geometric construction related to ''projection pursuit.'' They are both affine equivariant (coordinate-free) and have high breakdown point. The generalization of the median has a breakdown point of at least 1/(d + 1) in dimension d and the breakdown point can be as high as 1/3 under symmetry. In contrast, various estimators based on rejecting apparent outliers and taking the mean of the remaining observations have breakdown points not larger than 1/(d + 1) in dimension d.