Nonparametric estimation of directional highest density regions

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 contemplate...

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Bibliographic Details
Published in:Advances in data analysis and classification 2022-09, Vol.16 (3), p.761-796
Main Authors: Saavedra-Nieves, Paula, Crujeiras, Rosa M.
Format: Article
Language:English
Subjects:
Chemistry and Earth Sciences
Computer Science
Data Mining and Knowledge Discovery
Density
Economics
Finance
Health Sciences
Humanities
Insurance
Law
Management
Mathematics and Statistics
Medicine
Metric space
Nonparametric statistics
Physics
Plugs
Regular Article
Seismology
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
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Summary: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.
ISSN:1862-5347
1862-5355
DOI:10.1007/s11634-021-00457-4