纵向数据部分线性模型的一种稳健估计方法

A Robust Estimation Method for the Partial Linear Models with Longitudinal Data

摘要: 本文利用指数平方损失函数，针对纵向数据部分线性模型的参数部分提出了一种稳健的估计方法。首先通过核估计以及变换将非参部分消去，然后利用指数平方损失函数降低异常值的影响，构造出稳健的广义估计方程，最终推导出稳健的经验似然比函数，由此进行估计和统计推断。在一定正则条件下该估计具有相合性以及渐近正态性，蒙特卡洛模拟显示本文的方法具有稳健性以及较高的效率。

Abstract: Based on the exponential squared loss function, we propose a robust estimation method for the parametric parts in the partial linear models. By using the kernel approximation and transfor-mation, we first absorb the nonparametric part. Then by using the exponential squared loss func-tion to deduce the influence of outliers, we propose robust generalized estimation equations and empirical likelihood ratio function for estimation and inference. Under some regularity conditions, we show that the resulting estimators are consistent and asymptotic normality. Simulation results also illustrate the robustness and efficiency advantages of our method.