MALMEM: model averaging in linear measurement error models

• 成果类型: Article
• 署名作者: Zhang, Xinyu; Ma, Yanyuan; Carroll, Raymond J.
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12317
• 发表日期: 2019
• 页码: 763-779
• 关键词: logistic-regression; variable selection; prediction

摘要

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 n 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.