TY - JOUR
T1 - The multivariate L1-median and associated data depth
AU - Vardi, Yehuda
AU - Zhang, Cun Hui
PY - 2000/2/15
Y1 - 2000/2/15
N2 - This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-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 depth functions; and (iii) a simple closed-form formula of the L1- depth function for a given data cloud in R(d).
AB - This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-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 depth functions; and (iii) a simple closed-form formula of the L1- depth function for a given data cloud in R(d).
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U2 - 10.1073/pnas.97.4.1423
DO - 10.1073/pnas.97.4.1423
M3 - Article
C2 - 10677477
AN - SCOPUS:0034652134
SN - 0027-8424
VL - 97
SP - 1423
EP - 1426
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 4
ER -