An Efficient Method to Determine the Degree of Overlap of Two Multivariate Distributions

Abstract

Assessing the degree to which two probability density functions overlap is an important problem in several applications. Most of the existing proposals to tackle this problem can only deal with univariate distributions. For multivariate problems, existing methods often rely on unrealistic parametric distributional assumptions or are such that the corresponding univariate marginal measures are combined using ad hoc procedures. In this paper, we propose a new empirical measure of the degree of overlap of two multivariate distributions. Our proposal makes no assumptions on the form of the densities and can be efficiently computed even in relatively high-dimensional problems.