连续时间下非参数回归模型的误差密度估计的渐近均方误差(英文)

The Asymptotic Quadric Error of the Error-Density Estimator of Nonparameteric Regression in Continuous Time Processes

本文研究了连续时间下非参数回归的误差密度估计的收敛速度 ,给出了一定条件下误差密度的估计量 ^fT(x)的均方收敛速度 ,详细证明了以下重要结果 :E ^fT(x) -f(x) 2 =O(T-1/ 4)其中f(x)表示误差过程 {et,t≥ 0 }的未知密度 .

In this paper,we are mainly concerned with the rate of convergence of the error-density estimator of nonparametric regression in continuous time.We have proved that under suitable conditions the kernel density estimator T satisfies E T(x)-f(x)]2=O(T -1/4),where f denotes the unknown density of the error process {e t,t≥0}. 2=O(T -1/4),where f denotes the unknown density of the error process {e t,t≥0}.