A reliable data-based smoothing parameter selection method for circular kernel estimation

• Published in: Statistics and computing Vol. 34; no. 2
• Main Author: Ameijeiras-Alonso, Jose
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2024; Springer Nature B.V
• Subjects: Artificial Intelligence; Computer Science; Data smoothing; Density; Original Paper; Parameters; Plugs; Probability and Statistics in Computer Science; Selectors; Smoothing; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Plug-in rule; Circular data; Sheather and Jones bandwidth; Directional statistics; Kernel density estimation
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-024-10384-x

A new 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 accidents.