Kernel density estimation via diffusion
Z. I. Botev, J. F. Grotowski, and D. P. Kroese
Source: Ann. Statist. Volume 38, Number 5
(2010), 2916-2957.
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.
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Keywords: Nonparametric density estimation; heat kernel; bandwidth selection; Langevin process; diffusion equation; boundary bias; normal reference rules; data sharpening; variable bandwidth
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1281964340
Digital Object Identifier: doi:10.1214/10-AOS799
Zentralblatt MATH identifier: 1200.62029
Mathematical Reviews number (MathSciNet): MR2722460
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