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

TL;DR

This paper introduces a new data-driven method for selecting the smoothing parameter in circular kernel density estimation, improving accuracy and reliability for circular data analysis.

Contribution

It develops a circular version of Sheather and Jones bandwidths with plug-in rules, supported by theoretical analysis and real data illustration.

Findings

Proposed selectors outperform previous methods in simulations.

Theoretical analysis confirms asymptotic optimality.

Application to real data demonstrates practical utility.

Abstract

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 (DOI: 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.