左截断相依数据下非参数回归的局部M 估计

本文对左截断模型, 利用局部多项式的方法构造了非参数回归函数的局部M 估计. 在观察样本为平稳α-混合序列下, 建立了该估计量的强弱相合性以及渐近正态性. 模拟研究显示回归函数的局部M 估计比Nadaraya-Watson 型估计和局部多项式估计更稳健.

Local M-estimation of nonparametric regression with left-truncated and dependent data

In this paper,we construct a local M-estimator of nonparametric regression function by using the local polynomial technique for a left truncated model.We establish weak and strong consistency as well as asymptotic normality of the estimator when the observations form a stationary α-mixing sequence.Simulation study shows that the local M-estimator not only has advantages over the Nadaraya-Watson （NW） type and local polynomial （LP） estimators of the regression function,but also overcomes the lack of robustness for the NW type and LP estimators.