Kernel density estimation via diffusion

TL;DR

This paper introduces an adaptive kernel density estimator based on diffusion processes, which improves smoothing accuracy and reliability by using a pilot estimate and a novel bandwidth selection method, outperforming existing techniques.

Contribution

The paper proposes a new diffusion-based adaptive kernel density estimator with a plug-in bandwidth selection method that avoids normal reference rules.

Findings

Outperforms existing methods in accuracy

Provides more reliable density estimates

Demonstrates effectiveness through simulation studies

Abstract

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.