Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing

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Methodology and Computing in Applied Probability
Springer Nature

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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 H0 ∶ f = q. The performance of such testing procedure is show- cased 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

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Level sets semimetrics, Density estimation, Hypothesis testing, Permutation test, Microarray data

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