多维线性回归有偏子模型的多步调整相合推断

摘要

当协变量是高维时经常采用一个子模型作为工作模型.由于没有包含所有相关的变量,这个模型可能是有偏的.这样,基于子模型得到的参数估计可能是不相合的.在这篇文章中将首先通过多步调整方法构造一个条件无偏模型.与现有的方法相比,这个调整模型仅采用了一维非参估计.然后得到子模型参数的一个全局相合估计,而且获得了该估计的渐近正态性.数值模拟结果显示,基于调整模型的参数估计优于基于子模型和全模型的参数估计.%When the dimension of covariate is high, one usually uses a sub-model as working model. Such a model may be biased because not all relevant variables are contained in it. Thus the resulting estimator of parameter in the sub-model may be inconsistent. In this paper, we shall construct a conditionally unbiased model by multi-step-adjustment. Compared with the existing methods, the adjusted model only adopts univariate nonparametric estimations. A globally consistent estimator of parameter in the sub-model is constructed, and its asymptotic normality is also obtained. The simulation results further illustrate that the performance of the estimator based on the adjusted model is better than those of the estimators derived from the sub-model and the full model.