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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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    1. 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.
    2. Douglas Hayden & Peter Lazar & David Schoenfeld & for The Inflammation and the Host Response to Injury Investigators, 2009. "Assessing Statistical Significance in Microarray Experiments Using the Distance Between Microarrays," PLOS ONE, Public Library of Science, vol. 4(6), pages 1-7, June.
    3. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    4. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
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