K.C.S.Pillai Memorial Lecture

Iterated Multivariate Ranks - Truly Nonparametric Procedures?

John Marden
Professor
University of Illinois, Urbana-Champaign

Start Date and Time: Thu, 21 Mar 2002, 4:30 PM

End Date and Time: Thu, 21 Mar 2002, 5:30 PM

Venue: MATH 175

Refreshments: Refreshments will be available in MATH Library at 4:15 p.m.

Abstract:

Many hypothesis testing methods based on ranks are truly nonparametric in the sense that the distribution of the ranks under the null hypothesis do not depend on the underlying distribution of the data. In multivariate analysis, rank methods are typically not truly nonparametric. This talk explores an approach that is conjectured to give distribution-free multivariate ranks under very general conditions. The idea is to take the so-called spatial multivariate ranks, then the spatial ranks of the ranks, then the spatial ranks of those, etc., until these ranks converge. The conjecture is that the limit of these "iterated" ranks has a distribution that is independent of the underlying distribution of the original variables, depending only on the dimension. These limiting distributions turn out to be a type of null distribution for multidimensional scaling. Using this approach, one can easily perform truly nonparametric multivariate analogs of Kendall's tau test, the Wilcoxon/Mann-Whitney two-sample test, the Kruskal-Wallis test, and many others.