APPROXIMATION OF DENSITY-FUNCTIONS BY SEQUENCES OF EXPONENTIAL-FAMILIES
成果类型：
Article
署名作者：
BARRON, AR; SHEU, CH
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348252
发表日期：
1991
页码：
1347-1369
关键词：
摘要：
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.