一类部分函数线性模型的估计方法  

Estimation for the partial linear functional linear regression

作　　者：王晓光[1] 高黎[1] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024

出　　处：《高校应用数学学报（A辑）》2013年第3期253-265,共13页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11101063;61173103);中央高校基本科研业务费专项资金(DUT12LK29)

摘　　要：函数型数据是近年受到较多关注的一种新型数据类型,在因变量是标量变量、自变量包含标量变量和函数变量的回归问题中,提出了一类标量变量为线性形式且函数变量为部分线性形式的模型.基于核函数构造了该类模型的估计方法,在适当条件下研究了模型参数分量估计的渐近正态性和非参数分量估计的收敛速度.最后用模拟验证了估计方法在有限样本下的表现.Functional data is a new object of the attention of many researches recently.A more general class of functional linear models is introduced when the response is a scalar,some of the covariates are random vectors and some are functional.In this model,normal variables are related to the response linearly while functional variables have more complicated relationships,partially linear forms.An estimation procedure based on kernel smoothers is proposed,and asymptotic normality of the parametric part estimator and convergence rates of nonparametric parts estimator in the model are investigated under mild conditions.The finite sample performance of the proposed estimation method is illustrated with simulation studies.

关 键 词：函数数据 函数线性模型 核估计 收敛速度 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]