混合类型辅助变量下模型校准抽样估计研究

A Study on Sample Estimation of Model Calibration with Mixed Auxiliary Variables

在超总体模型中,一般用于构建模型的辅助变量多为连续型变量,对混合类型辅助变量的模型研究较少。为了同时利用与研究变量相关的连续型和离散型辅助变量的信息,本文提出在模型校准的框架下,利用非参数核回归方法,得到混合类型辅助变量下的模型校准估计量。研究证明,该估计量是渐进设计无偏、设计一致和渐进正态的,并给出了估计量的方差和方差的估计量。数值模拟的结果显示,本文在总体回归函数为线性和非线性的情况下,估计效果均有所提高。此外,通过CLHLS数据的验证也表明该估计量的效果优于仅利用连续型辅助变量的估计量。

In the super population model, the continuous variables are generally used as the auxiliary variables to build up models. However, there are very rare cases to study the models with the mixed auxiliary variables. In order to fully use the correlative information both related to continuous and discrete variables, a nonparametric model calibration estimator with mixed auxiliary variables is proposed in this paper by applying the methodology of nonparametric kernel regression under the framework of model calibration. The proposed estimator has been proved to be asymptotically unbiased, consistent and asymptotically normal as it is designed, together with its variance and its variance estimator.. The study with simulation data shows that the effect of the proposed estimator has been much improved whenever the total regression function is linear or nonlinear. In addition, the validation study with the CLHLS data justifies that the proposed estimator is better than that based only on the continuous auxiliary variables.