Saavedra Nieves, PaulaCrujeiras Casais, Rosa María2023-02-132023-02-132021Saavedra-Nieves, P., Crujeiras, R.M. Nonparametric estimation of directional highest density regions. Adv Data Anal Classif 16, 761–796 (2022). https://doi.org/10.1007/s11634-021-00457-41862-5347http://hdl.handle.net/10347/30065Highest 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 seismologyeng© 2021 The Authors. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/BootstrapConfidence regionsDirectional dataHausdorff distanceHighest density regionsKernel density estimationLevel setsjournal article10.1007/s11634-021-00457-41862-5355open access