ESTIMATION IN FUNCTIONAL REGRESSION FOR GENERAL EXPONENTIAL FAMILIES

• 成果类型: Article
• 署名作者: Dou, Winston Wei; Pollard, David; Zhou, Harrison H.
• 署名单位: Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1027
• 发表日期: 2012
• 页码: 2421-2451
• 关键词: LINEAR-REGRESSION; CONVERGENCE; prediction; models; rates

摘要

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A change-of-measure argument, inspired by Le Cam's theory of asymptotic equivalence, is used to eliminate the bias caused by the nonlinearity of exponential family models.