Ameijeiras Alonso, José2024-05-162024-05-162024Ameijeiras-Alonso, J. A reliable data-based smoothing parameter selection method for circular kernel estimation. Stat Comput 34, 73 (2024). https://doi.org/10.1007/s11222-024-10384-x0960-3174http://hdl.handle.net/10347/33860new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper provides a circular version of the well-known Sheather and Jones bandwidths (J R Stat Soc Ser B Stat Methodol 53(3):683–690, 1991. https://doi.org/10.1111/j.2517-6161.1991.tb01857.x), with direct and solve-the-equation plug-in rules. Theoretical support for our developments, related to the asymptotic mean squared error of the estimator of the density, its derivatives, and its functionals, for circular data, are provided. The proposed selectors are compared with previous data-based smoothing parameters for circular kernel density estimation. This paper also contributes to the study of the optimal kernel for circular data. An illustration of the proposed plug-in rules is also shown using real data on the time of car accidentsengAtribución 4.0 InternacionalThis 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/http://creativecommons.org/licenses/by/4.0/Circular dataDirectional statisticsKernel density estimationPlug-in ruleSheather and Jones bandwidthjournal article10.1007/s11222-024-10384-x1573-1375open access