中文摘要：

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.

英文摘要：

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.