The multivariate L_{1}median and associated data depth
Abstract
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 &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 dept functions; and (iii) a simple closedform formula of the L_{1}depth function for a given data cloud in &R;^{d}.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 February 2000
 DOI:
 10.1073/pnas.97.4.1423
 Bibcode:
 2000PNAS...97.1423V
 Keywords:

 Statistics