Approximation of Density Functions by Sequences of Exponential Families Export

@article{citeulike:157632, abstract = {Probability density functions are estimated by the method of maximum likelihood in sequences of regular exponential families. This method is also familiar as entropy maximization subject to empirical constraints. The approximating families of log-densities that we consider are polynomials, splines and trigonometric series. Bounds on the relative entropy (Kullback-Leibler distance) 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.}, author = {Barron, Andrew R. and Sheu, Chyong-Hwa}, citeulike-article-id = {157632}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/2241953}, citeulike-linkout-1 = {http://www.jstor.org/stable/2241953}, citeulike-linkout-2 = {http://www.cs.orst.edu/~bulatov/papers/barron-approximation.pdf}, doi = {10.2307/2241953}, journal = {The Annals of Statistics}, keywords = {density, exponential-families, nonparametric}, number = {3}, pages = {1347--1369}, posted-at = {2005-09-03 22:47:16}, priority = {2}, title = {Approximation of Density Functions by Sequences of Exponential Families}, url = {http://dx.doi.org/10.2307/2241953}, volume = {19}, year = {1991} }

TY - JOUR ID - citeulike:157632 L3 - citeulike-article-id:157632 N2 - Probability density functions are estimated by the method of maximum likelihood in sequences of regular exponential families. This method is also familiar as entropy maximization subject to empirical constraints. The approximating families of log-densities that we consider are polynomials, splines and trigonometric series. Bounds on the relative entropy (Kullback-Leibler distance) 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. IS - 3 JF - The Annals of Statistics EP - 1369 TI - Approximation of Density Functions by Sequences of Exponential Families VL - 19 SP - 1347 KW - density KW - exponential-families KW - nonparametric AU - Barron, Andrew AU - Sheu, Chyong-Hwa PY - 1991/// UR - http://dx.doi.org/10.2307/2241953 ER -