A New Distance for Probability Measures Based on the Estimation of Level Sets

Alberto Muñoz, Gabriel Martos, Javier Arriero, Javier Gonzalez

Abstract: In this paper we propose to consider Probability Measures (PM) as generalized functions belonging to some functional space endowed with an inner product. This approach allows to introduce a new family of distances for PMs. We propose a particular (non parametric) metric for PMs belonging to this class, based on the estimation of density level sets. Some real and simulated data sets are used for a first exploration of its performance.