固定设计函数型非参数回归模型的估计  

Fixed Design Type of Function-based Estimates of Non-parametric RegressionModel

作　　者：陆晓恒[1,2] 潘阳丽[2] 凌能祥[2] 

机构地区：[1]铜陵学院数学与计算机科学系,安徽铜陵244000 [2]合肥工业大学数学学院,安徽合肥230009

出　　处：《应用数学》2013年第2期395-403,共9页Mathematica Applicata

基　　金：教育部人文社科规划基金项目(10YJA910005);安徽省自然科学基金项目(11040606M03)

摘　　要：本文研究一类固定设计函数型非参数回归模型回归算子的估计问题,其中,解释变量X是取值于某函数空间的函数型变量,响应变量Y为实值随机变量,在误差是一弱平稳线性过程及适当的条件下,获得未知回归函数算子估计量的相合性及其收敛速度和渐近正态性,推广了现有文献中的相关结果.In this paper, we investigate the estimation of regression operator for the fixeddesign of functional nonparametrie model, where the explanatory variable X takes value in some functional space and the response Y is a real random variable. When the error satisfies weekly stationary linear process, we obtain the consistency and the convergence rate as well as asymptotic normality of the regression estimator under suitable conditions, which expand the results of the existing literatures. That is the main contribitions of the paper.

关 键 词：函数型数据 线性过程 回归模型 相合性 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]