相依误差下部分函数型线性模型的估计  

Partial Functional Linear Models with Dependent Errors

作　　者：王亚飞[1] 杜江[2] 张忠占[2] WANG YAFEI DU JIANG ZHANG ZHONGZHAN(College of Applied Sciences, Beijing University of Technology, Beijing 100124, China College of Applied Sciences, Beijing University of Technology, Collaborative Innovation Center on Capital Social Construction and Social Management, Beijing 100124, China)

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]北京工业大学应用数理学院,首都社会建设和社会管理协同创新中心,北京100124

出　　处：《应用数学学报》2017年第1期49-65,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11271039);高等学校博士学科点专项科研基金(20131103110027)资助项目

摘　　要：本文研究当误差序列为平稳的a-混合序列时,部分函数型线性模型的估计问题,基于用Karhunen-Loeve展开来逼近斜率函数的思想,给出了未知参数和斜率函数的估计方法,并进一步建立了参数估计量的渐近正态性和斜率函数估计量的收敛速度.最后用模拟研究和具体实例说明了估计方法的良好表现以及相依误差结构对估计量所带来的影响.In this paper, we study the estimation of partial functional linear regression models with stationary α-mixing random error sequence. With approximating to the slope function by the Karhunen-Loeve expansion, we propose an estimation method for the unknown parameters and the slope function. The asymptotic normality of the proposed parameter estimators and the convergence rate of the slope function estimator are established. Intensive simulation experiments and real data analysis are conducted to show that the proposed method performs well with a finite sample.

关 键 词：渐近正态性 Α-混合序列 主成分 收敛速度 

分 类 号：O177.2[理学—数学]