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Barron, Andrew Sheu, Chyong-Hwa 2011-05-07T12:49:35Z 2011-05-07T12:49:35Z 10000-01-01 1990 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. Made available in DSpace on 2011-05-07T12:49:35Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026321.pdf: 2538015 bytes, checksum: 484ae5fe910d009aa75229d877057ad6 (MD5) Previous issue date: 1990 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:46:21Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:20:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9026321 (UMI)AAI9026321 http://hdl.handle.net/2142/20798 eng Copyright 1990 Sheu, Chyong-Hwa Statistics Density estimation with Kullback-Leibler loss text Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.