Open Access
October 2010 Kernel density estimation via diffusion
Z. I. Botev, J. F. Grotowski, D. P. Kroese
Ann. Statist. 38(5): 2916-2957 (October 2010). DOI: 10.1214/10-AOS799


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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Z. I. Botev. J. F. Grotowski. D. P. Kroese. "Kernel density estimation via diffusion." Ann. Statist. 38 (5) 2916 - 2957, October 2010.


Published: October 2010
First available in Project Euclid: 16 August 2010

zbMATH: 1200.62029
MathSciNet: MR2722460
Digital Object Identifier: 10.1214/10-AOS799

Primary: 62G07 , 62G20
Secondary: 35K05 , 35K15 , 60J60 , 60J70

Keywords: Bandwidth selection , Boundary bias , data sharpening , diffusion equation , heat kernel , Langevin process , Nonparametric density estimation , normal reference rules , variable bandwidth

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 5 • October 2010
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