Testing for proportionality of multivariate dispersion structures using interdirections

Knowing whether the dispersion structures of two elliptically symmetric populations are proportional is an important problem in multivariate data analysis. Since the problem is invariant under nonsingular transformations it is possible to reduce it to the situation where one population is spherically symmetric while the other has a diagonal dispersion structure. In this article we develop a nonparametric test procedure based on the idea of inter directions, introduced by Randies (1989) in the context of multivariate sign tests. The findings of this article also enhance the possibility of developing a technology for robust multivariate data analysis using such fundamentally geometric concepts.