频率模型平均估计近年来受到较多关注, 但目前文献对有测量误差数据 的模型平均估计方法研究较少. 文章考虑异方差线性测量误差模型平均估计方法, 基于Mallows权重选择准则提出了新的模型平均估计, 并在理论上证明了其渐近最优性. 模 拟结果表明, 新方法相较于一些常用的模型平均(如SAIC, SBIC)与模型选择方法(如AIC, BIC)具有较大优 势.

Frequentist model averaging estimation receives much attention in recent years, but there is rare investigation for data with measurement errors. In this paper, the method of model averaging is applied to heteroscedastic linear models with measurement errors, and we obtain the new model averaging estimator based on the Mallows criterion. The asymptotic optimality of the estimator is proved. In a simulation experiment, we show that the new method performs better than some commonly used model averaging methods (such as SAIC and SBIC) and model selection methods (such as AIC and BIC).