Nonparametric estimation of directional highest density regions

Paula Saavedra-Nieves () and Rosa M. Crujeiras
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Paula Saavedra-Nieves: Universidade de Santiago de Compostela
Rosa M. Crujeiras: Universidade de Santiago de Compostela

Advances in Data Analysis and Classification, 2022, vol. 16, issue 3, No 10, 796 pages

Abstract: Abstract Highest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismology.

Keywords: Bootstrap; Confidence regions; Directional data; Hausdorff distance; Highest density regions; Kernel density estimation; Level sets; 62G05; 62G07 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11634-021-00457-4

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