变量有误差的变系数部分线性模型的估计

Estimation of Varying-Coefficient Partially Linear Model with Measurement Error in the Parametric Part

研究了变系数部分线性回归模型的估计方法.在误差为条件异方差的情况下,用一般序列估计方法得到的参数估计是有效的.但实际应用中,协变量往往有测量误差,若忽略测量误差,由一般序列估计得到的估计是有偏的.通过对一般序列估计进行适当修正,得到的参数部分的估计具有一致性和渐近正态性,同时也讨论了非参数部分估计的收敛速度.最后,在有限样本下通过Monte Carlo模拟验证了修正后的估计效果.

This paper mainly discusses the estimation method for varying-coefficient partially linear models.When the error is conditionally heteroskedastic,we can obtain a semiparametrically efficient estimator by the general series estimation method.But in practical application,the covariates are always measured with errors.If we ignore the measurement errors,the general series estimator will be biased.In this paper,we consider how to obtain an unbiased estimator on the foundation of general series method by suitable correction of the general series estimation.Moreover,consistency and asymptotic normality of the parametric estimator are investigated.Meanwhile,we discuss the rate of convergence in the nonparametric part.Finally,some simulation studies are proposed to verify the effect of the modified estimation on the finite sample condition.