非参数函数型递归核估计的收敛速度

Convergence rate of recursive kernel estimation of nonparametric regression with functional responses

文章考虑当响应变量和解释变量都是函数型时的非参数核回归模型,将经典的N-W核估计量推广为一族递归核估计量,并且利用Kolmogorov熵的方法和函数型数据的基本方法,得到递归估计量在独立情形下的一致收敛速度。

T his paper considers the nonparametric kernel regression model w hen the response variable and the explanatory variable are functional .The classical N‐W kernel estimator is generalized to a class of recursive kernel estimator ,and by using the Kolmogorov’s entropy and some basic methods of functional data ,the rate of almost uniform complete convergence of the recursive estimator is obtained for independent identically distributed（i .i .d .） functional time series data .