基于平稳遍历函数型数据改良核回归估计渐近正态性

Asymptotic normality of modified kernel regression estimation for functional stationary ergodic data

文章基于解释变量X具有函数特征而响应变量Y取值于实数空间R的条件下,研究了基于平稳遍历函数型数据改良核回归估计的渐近性质。利用经典的N-W核估计的方法构造了回归函数r(x)的改良核估计,在一定的条件下,应用鞅差中心极限定理建立了基于平稳遍历函数型数据改良核回归估计的渐近正态性,从而推广了现有文献中的相关结果。

In this paper, the asymptotic property of modified kernel regression estimation for functional stationary ergodic data is researched when the explanatory variable X has functional characteristic and the response variable Y is a scalar in real-value space R. Specifically, the modified kernel estimation of the regression function r（x） is constructed by using the classic Nadaraya-Watson estimator. Under certain conditions, the asymptotic normality of modified kernel regression estimation for functional stationary ergodic data is established by applying the martingale difference central limit theorem, which extends the a-mixing data to the functional stationary ergodic data.