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

arXiv: https://arxiv.org/abs/1306.0517 · HTML: https://mlsanity.com/paper/1306.0517/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2013.

## Built on by (most cited first, 4 of 4)

- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [The EM Perspective of Directional Mean Shift Algorithm](https://mlsanity.com/paper/2101.10058/) (2021)
- [Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach](https://mlsanity.com/paper/2110.08505/) (2021)
- [GLASS: Graph-Language Alignment with Spherical Scoring for Transferable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2609.05253/) (2026)

## Abstract (arXiv)

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.