Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing

Alberto Muñoz, Gabriel Martos () and Javier Gonzalez
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Alberto Muñoz: Universidad Carlos III de Madrid
Gabriel Martos: Universidad Torcuato Di Tella
Javier Gonzalez: Microsoft Research Cambridge

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-17

Abstract: Abstract 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 $$H_0: f=q$$ 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.

Keywords: Level sets semimetrics; Density estimation; Hypothesis testing; Permutation test; Microarray data; 62 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-09990-5

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