Vardi, Yehuda; Zhang, Cun-Hui The multivariate \(L_1\)-median and associated data depth. (English) Zbl 1054.62067 Proc. Natl. Acad. Sci. USA 97, No. 4, 1423-1426 (2000). Summary: This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the \(L_1\)-median of a data cloud in \(\mathbb R^d\), 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 depth functions; and (iii) a simple closed-form formula of the \(L_1\)-depth function for a given data cloud in \(\mathbb R^d\). Cited in 110 Documents MSC: 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62H99 Multivariate analysis PDFBibTeX XMLCite \textit{Y. Vardi} and \textit{C.-H. Zhang}, Proc. Natl. Acad. Sci. USA 97, No. 4, 1423--1426 (2000; Zbl 1054.62067) Full Text: DOI Link