具有非参数AR(1)误差的回归模型的局部线性估计

Local Linear Estimation in the Presence of Nonparametric AR(1) Errors

考虑随机设计下具有一阶非参数自回归误差的线性回归模型,构造了参数和非参数函数的局部线性估计。在适当的条件下,证明了参数估计量的渐近正态性,并给出了非参数函数估计的收敛速度。模拟算例表明局部线性方法优于核方法。

Under the random-design, linear regression model with first-order nonparametric autoregressive errors is considered in this paper. We construct the local linear estimators of parameter and nonparametric function under suitable conditions and prove the asymptotic normality of nonparameter. We also give the estimator＇s convergence rate of nonparametric function. Simulating examples show that the local linear estimators are superior to the kernel estimators.