Exact risk improvement of bandwidth selectors for kernel density estimation with directional data

TL;DR

This paper introduces new bandwidth selectors for kernel density estimation with directional data, demonstrating superior performance through simulation and real data applications, especially the one based on exact error expressions.

Contribution

It proposes novel bandwidth selectors using asymptotic and exact error formulas tailored for directional data, outperforming existing methods in various scenarios.

Findings

Exact error-based selector shows best performance in simulations.

Proposed selectors outperform existing rules in diverse directional scenarios.

Effective application demonstrated on real circular and spherical data.

Abstract

New bandwidth selectors for kernel density estimation with directional data are presented in this work. These selectors are based on asymptotic and exact error expressions for the kernel density estimator combined with mixtures of von Mises distributions. The performance of the proposed selectors is investigated in a simulation study and compared with other existing rules for a large variety of directional scenarios, sample sizes and dimensions. The selector based on the exact error expression turns out to have the best behaviour of the studied selectors for almost all the situations. This selector is illustrated with real data for the circular and spherical cases.