带有完全随机缺失协变量的广义线性模型平均方法研究

Model Averaging for Generalized Linear Model with Covariates That are Missing Completely at Random

目前,已有大量关于模型平均方法的研究,其中包括对线性和广义线性模型平均估计以及协变量带有缺失数据的线性模型的研究。但是,关于协变量带有缺失数据的广义线性模型尚未得到研究。本文探讨的是带有完全随机缺失协变量的广义线性模型的模型平均估计。我们提出了一个模型平均估计方法并且证明了在一定假设条件下,相应的模型平均估计量具有渐近最优性。模拟结果显示在大多数情况下,本文方法相较于其他方法表现更好。

At present,there are amount of researches on model averaging,including the studies of linear and generalized linear models and the linear models with covariates missed.However,the model averaging method for generalized linear models with missing data of covariates has not been studied.In this paper,we consider the estimation of generalized linear models with covariates that are missing completely at random.We propose a model averaging estimation method and prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions.Simulation results illustrate that this method has better performance than other alternatives under most situations.