Exponential inequalities for martingales, with application to maximum likelihood estimation for counting processes
成果类型：
Article
署名作者：
VandeGeer, S
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176324323
发表日期：
1995
页码：
1779-1801
关键词：
摘要：
We obtain an exponential probability inequality for martingales and a uniform probability inequality for the process integral gdN, where N is a counting process and where g varies within a class of predictable functions g. For the latter, we use techniques from empirical process theory. The uniform inequality is shown to hold under certain entropy conditions on g. As an application, we consider rates of convergence for (nonparametric) maximum likelihood estimators for counting processes. A similar result for discrete time observations is also presented.