A maximal, inequality for continuous martingales and M-estimation in a Gaussian white noise model

• 成果类型: Article
• 署名作者: Nishiyama, Y
• 署名单位: Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1018031212
• 发表日期: 1999
• 页码: 675-696
• 关键词: diffusion-processes; REGRESSION FUNCTION; CONVERGENCE; rates; jump

摘要

Some sufficient conditions to establish the rate of convergence of certain M-estimators in a Gaussian white noise model are presented. They are applied to some concrete problems, including jump point estimation and nonparametric maximum Likelihood estimation, for the regression function. The results are shown by means of a maximal inequality for continuous martingales and some techniques developed recently in the context of empirical processes.