Bump hunting through density curvature features

José E. Chacón () and Javier Fernández Serrano ()
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José E. Chacón: Universidad de Extremadura
Javier Fernández Serrano: Universidad Autónoma de Madrid

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 4, No 9, 1275 pages

Abstract: 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.

Keywords: Bump hunting; Concavity; Gaussian curvature; Kernel density derivative estimation; Laplacian; Mean curvature; Primary 62G05; 62G20; 60D05; 62R07 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00872-z

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