2000/02/15 by Yehuda Vardi, Cun-Hui Zhang · 4 citations
Mathematics · Decision Sciences · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Statistical Methods and Inference
paper · doi:10.1073/pnas.97.4.1423
openalex publication_date 2000/02/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/26
This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in Rd, a problem that can be traced to Fermat and has fascinated applied mathematicians for over three centuries; (ii) a new general definition for depth functions, as functions of multivariate medians, so that different definitions of medians will, correspondingly, give rise to different dept functions; and (iii) a simple closed-form formula of the L1-depth function for a given data cloud in Rd.