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Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing

Author

Listed:
  • Alberto Muñoz

    (Universidad Carlos III de Madrid)

  • Gabriel Martos

    (Universidad Torcuato Di Tella)

  • Javier Gonzalez

    (Microsoft Research Cambridge)

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.

Suggested Citation

  • Alberto Muñoz & Gabriel Martos & Javier Gonzalez, 2023. "Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09990-5
    DOI: 10.1007/s11009-023-09990-5
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    References listed on IDEAS

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    4. Yen-Chi Chen & Christopher R. Genovese & Larry Wasserman, 2017. "Density Level Sets: Asymptotics, Inference, and Visualization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1684-1696, October.
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