Yale University
Department of Statistics
Seminar

Monday, September 25, 2000
A new algorithm for the L_1 multivariate mendian, and a new concept of data-depth in mutivariate data-analysis
Yehuda Vardi
Department of Statistics
Rutgers University

Seminar to be held in Room 107, 24 Hillhouse at 4:15 pm


A new algorithm for the L_1 multivariate mendian, and a new concept of data-depth in mutivariate data-analysis
The Fermat-Weber location problem (also known as the mutivariate L_1 median, and the Euclidean Steiner problem) has been around for nearly three centuries, and the most widely used algorithm for finding it is the well known Weiszfeld (1938) algorithm, which may actually stop before hitting the L_1 median. We propose a new algorithm (equally simple and elegant) which is guarantied to converge monotonically to the desired median. We further define a new concept for 'data-depth' of a mutivariate distribution, and show that for the L_1 and other multivariate medians this new definition gives simple, closed-form, formulae which are easy to compute in any dimension, making the new concept a practical multivariate data-analytic tool.