The Annals of Statistics

Kernel density estimation via diffusion

Z. I. Botev, J. F. Grotowski, and D. P. Kroese

Full-text: Open access

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.

Article information

Source
Ann. Statist. Volume 38, Number 5 (2010), 2916-2957.

Dates
First available in Project Euclid: 16 August 2010

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

Subjects
Primary: 62G07: Density estimation 62G20: Asymptotic properties
Secondary: 35K05: Heat equation 35K15: Initial value problems for second-order parabolic equations 60J60: Diffusion processes [See also 58J65] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]

Keywords
Nonparametric density estimation heat kernel bandwidth selection Langevin process diffusion equation boundary bias normal reference rules data sharpening variable bandwidth

Citation

Botev, Z. I.; Grotowski, J. F.; Kroese, D. P. Kernel density estimation via diffusion. Ann. Statist. 38 (2010), no. 5, 2916--2957. doi:10.1214/10-AOS799. http://projecteuclid.org/euclid.aos/1281964340.


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