FOCUSED INFORMATION CRITERION AND MODEL AVERAGING FOR GENERALIZED ADDITIVE PARTIAL LINEAR MODELS

• 成果类型: Article
• 署名作者: Zhang, Xinyu; Liang, Hua
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Rochester
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS832
• 发表日期: 2011
• 页码: 174-200
• 关键词: semiparametric regression; polynomial splines; tensor-products; selection; inference

摘要

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.