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Bump hunting through density curvature features

Author

Listed:
  • José E. Chacón

    (Universidad de Extremadura)

  • Javier Fernández Serrano

    (Universidad Autónoma de Madrid)

Abstract

Bump hunting deals with finding in sample spaces meaningful data subsets known as bumps. These have traditionally been conceived as modal or concave regions in the graph of the underlying density function. We define an abstract bump construct based on curvature functionals of the probability density. Then, we explore several alternative characterizations involving derivatives up to second order. In particular, a suitable implementation of Good and Gaskins’ original concave bumps is proposed in the multivariate case. Moreover, we bring to exploratory data analysis concepts like the mean curvature and the Laplacian that have produced good results in applied domains. Our methodology addresses the approximation of the curvature functional with a plug-in kernel density estimator. We provide theoretical results that assure the asymptotic consistency of bump boundaries in the Hausdorff distance with affordable convergence rates. We also present asymptotically valid and consistent confidence regions bounding curvature bumps. The theory is illustrated through several use cases in sports analytics with datasets from the NBA, MLB and NFL. We conclude that the different curvature instances effectively combine to generate insightful visualizations.

Suggested Citation

  • José E. Chacón & Javier Fernández Serrano, 2023. "Bump hunting through density curvature features," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1251-1275, December.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:4:d:10.1007_s11749-023-00872-z
    DOI: 10.1007/s11749-023-00872-z
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    References listed on IDEAS

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    1. Mammen, Enno & Polonik, Wolfgang, 2013. "Confidence regions for level sets," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 202-214.
    2. 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.
    3. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
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