Non-linear kernel density estimation for binned data: convergence in entropy.

Blower, Gordon and Kelsall, Julia E. (2002) Non-linear kernel density estimation for binned data: convergence in entropy. Bernoulli, 8 (4). pp. 423-449. ISSN 1350-7265

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Abstract

A method is proposed for creating a smooth kernel density estimate from a sample of binned data. Simulations indicate that this method produces an estimate for relatively finely binned data which is close to what one would obtain using the original unbinned data. The kernel density estimate {\hat f}\, is the stationary distribution of a Markov process resembling the Ornstein-Uhlenbeck process. This {\hat f}\, may be found by an iteration scheme which converges at a geometric rate in the entropy pseudo-metric, and hence in L1\, and transportation metrics. The proof uses a logarithmic Sobolev inequality comparing relative Shannon entropy and relative Fisher information with respect to \hat f.

Item Type: Article Bernoulli binned data ; density estimation ; kernel estimation ; logarithmic Sobolev inequality ; transportation Q Science > QA Mathematics Faculty of Science and Technology > Mathematics and Statistics 19254 ep_ss_importer 14 Nov 2008 15:14 Yes Published 07 Jan 2015 13:09 http://eprints.lancs.ac.uk/id/eprint/19254