RT Journal Article
T1 Nonparametric estimation of directional highest density regions
A1 Saavedra Nieves, Paula
A1 Crujeiras Casais, Rosa María
K1 Bootstrap
K1 Confidence regions
K1 Directional data
K1 Hausdorff distance
K1 Highest density regions
K1 Kernel density estimation
K1 Level sets
AB 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
PB Springer
SN 1862-5347
YR 2021
FD 2021
LK http://hdl.handle.net/10347/30065
UL http://hdl.handle.net/10347/30065
LA eng
NO Saavedra-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/s11634-021-00457-4
NO Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. R.M. Crujeiras and P. Saavedra-Nieves acknowledge the financial support of Ministerio de Economía y Competitividad and Ministerio de Ciencia e Innovación of the Spanish government under grants MTM2016-76969P, MTM2017-089422-P, PID2020-118101GB-I00 and PID2020-116587GB-I00 and ERDF. Authors also thank Elena Vázquez Abal for her help, Prof. Felicita Scapini for providing the sandhoppers data (collected under the support of the European Project ERB ICI8-CT98-0270), the computational resources of the CESGA Supercomputing Center and the referees for the constructive comments which have improved the paper
DS Minerva
RD 25 abr 2026