We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.
"Kernel density estimation via diffusion." Ann. Statist. 38 (5) 2916 - 2957, October 2010. https://doi.org/10.1214/10-AOS799