Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing Articles uri icon

publication date

  • March 2023


  • 1


  • 25

International Standard Serial Number (ISSN)

  • 1387-5841

Electronic International Standard Serial Number (EISSN)

  • 1573-7713


  • 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: 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.


  • density estimation; hypothesis testing; level sets semimetrics; microarray data; permutation test