Nonparametric Density Estimation via Diffusion Mixing

Botev, Z. I. (2007). Nonparametric Density Estimation via Diffusion Mixing. Postgraduate series , Department of Mathematics, The University of Queensland.

Attached Files (Some files may be inaccessible until you login with your UQ eSpace credentials)
Name Description MIMEType Size Downloads
diffusion_estimator.pdf diffusion_estimator.pdf Click to show the corresponding preview/stream application/pdf 200.22KB 1209
Author Botev, Z. I.
Title Nonparametric Density Estimation via Diffusion Mixing
School, Department or Centre Department of Mathematics
Institution The University of Queensland
Series Postgraduate series
Publication date 2007-11-20
Subject 230000 Mathematical Sciences
230203 Statistical Theory
230204 Applied Statistics
Abstract/Summary Suppose we are given empirical data and a prior density about the distribution of the data. We wish to construct a nonparametric density estimator that incorporates the prior information. We propose an estimator that allows for the incorporation of prior information in the density estimation procedure within a non-Bayesian framework. The prior density is mixed with the available empirical data via a Langevin diffusion process. The diffusion process is constructed so that the prior density is the limiting and stationary distribution of the process. We analyze the asymptotic bias and variance properties of the estimator and compare them with the properties of the standard density estimators. We present simulation examples in which the proposed estimator outperforms the standard estimation procedures in terms of accuracy.
Keyword nonparametric density estimation
Langevin process
heat kernel
bandwidth selection
diffusion equation
References [1] I.S. Abramson. On bandwidth variation in kernel estimates—a square root law. Ann. Stat., 10:1217–1223, 1982. [2] Chaudhuri and Marron. Scale space view of of curve estimation. The Annals of Statistics, 2000. [3] G. R. Gavalas and Y. C. Yortsos. Short-time asymptotic solutions of the heat equation with spatially varying coefficients. J. Inst. Math. Appl., 26(3):209–219, 1980. [4] J. S. Marron and M. P. Wand. Exact mean integrated error. The Annals of Statistics, 20:712–736, 1992. [5] I.J. McKay M.C. Jones and T.C.Hu. Variable location and scale kernel density esti- mation. Annals of the Institute of Statistical Mathematics, 46:521–535, 1994. [6] M. Samiuddin and G. M. El-Sayyad. On nonparametric kernel density estimates. Biometrika, 77:865, 1990. [7] S. J. Sheather and M. C. Jones. A reliable data-based bandwidth selection method for kernel density estimation. J.R.Statist.Soc.B, 53:683–690, 1991.

Document type: Working Paper
Collection: School of Physical Sciences Publications
 
Versions
Version Filter Type
Citation counts: Google Scholar Search Google Scholar
Access Statistics: 1397 Abstract Views, 1238 File Downloads  -  Detailed Statistics
Created: Tue, 20 Nov 2007, 13:45:54 EST by Zdravko Botev