Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing

In this paper we introduce a novel family of level sets semimetrics for density functions and address subtleties entailed in the estimation and computation of such semimetrics. Given data drawn from f and q , two unknown density functions, we consider different level set semimetrics so to test the null hypothesis H_0: f=q . The performance of such testing procedure is showcased in a Monte Carlo simulation study. Using the methods developed in the paper, we assess differences in gene expression profiles between two groups of patients with different respiratory recovery patterns in a clinical study; and find significant differences between the 15 top–ranked genes density profiles corresponding to the two groups.