Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing
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Methodology and Computing in Applied Probability
Springer Nature
Springer Nature
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 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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Keywords
Level sets semimetrics, Density estimation, Hypothesis testing, Permutation test, Microarray data