Zhang Xinyu, Ma Yanyuan, Carroll Raymond J
University of Science and Technology of China, Hefei, and Chinese Academy of Sciences, Beijing, People's Republic of China.
Pennsylvania State University, University Park, USA.
J R Stat Soc Series B Stat Methodol. 2019 Sep;81(4):763-779. doi: 10.1111/rssb.12317. Epub 2019 Jun 2.
We develop model averaging estimation in the linear regression model where some covariates are subject to measurement error. The absence of the true covariates in this framework makes the calculation of the standard residual-based loss function impossible. We take advantage of the explicit form of the parameter estimators and construct a weight choice criterion. It is asymptotically equivalent to the unknown model average estimator minimizing the loss function. When the true model is not included in the set of candidate models, the method achieves optimality in terms of minimizing the relative loss, whereas, when the true model is included, the method estimates the model parameter with root rate. Simulation results in comparison with existing Bayesian information criterion and Akaike information criterion model selection and model averaging methods strongly favour our model averaging method. The method is applied to a study on health.
我们在一些协变量存在测量误差的线性回归模型中开发了模型平均估计。在此框架中，由于不存在真实协变量，使得基于标准残差的损失函数的计算变得不可能。我们利用参数估计量的显式形式，并构建了一个权重选择标准。它在渐近意义上等同于使损失函数最小化的未知模型平均估计量。当真实模型不包含在候选模型集中时，该方法在最小化相对损失方面达到最优，而当真实模型包含在内时，该方法以根速率估计模型参数。与现有的贝叶斯信息准则和赤池信息准则模型选择及模型平均方法相比，模拟结果强烈支持我们的模型平均方法。该方法应用于一项健康研究。
