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Title:Density estimation with Kullback-Leibler loss
Author(s):Sheu, Chyong-Hwa
Doctoral Committee Chair(s):Barron, Andrew
Department / Program:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:Probability density functions are estimated by the method of maximum likelihood in sequences of regular exponential families. The approximation families of log-densities that we consider are polynomials, splines, and trigonometric series. Bounds on the relative entropy (Kullback-Leibler number) between the true density and the estimator are obtained and rates of convergence are established for log-density functions assumed to have square integrable derivatives. The relative entropy risk between true probability density function and the estimator is shown to converge to zero at a desired rate. The idea is to select n samples from the true distribution and choose the estimator which is the maximum posterior likelihood estimator in certain regular m-parameter exponential families, given that a Gaussian distribution is the prior on the parameter space. The implications for universal source coding and portfolio selection are discussed.
Issue Date:1990
Rights Information:Copyright 1990 Sheu, Chyong-Hwa
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9026321
OCLC Identifier:(UMI)AAI9026321

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