ESTIMATION AND INFERENCE IN GENERALIZED ADDITIVE COEFFICIENT MODELS FOR NONLINEAR INTERACTIONS WITH HIGH-DIMENSIONAL COVARIATES

• 成果类型: Article
• 署名作者: Ma, Shujie; Carroll, Raymond J.; Liang, Hua; Xu, Shizhong
• 署名单位: University of California System; University of California Riverside; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney; George Washington University; University of California System; University of California Riverside
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1344
• 发表日期: 2015
• 页码: 2102-2131
• 关键词: VARIABLE SELECTION; polynomial spline; PENALIZED LIKELIHOOD; regression-models; local asymptotics; oracle properties; confidence bands; diverging number; index models; obesity

摘要

In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the large p small n setting. The procedure is shown to be consistent for model structure identification. Further, we construct simultaneous confidence bands for the coefficient functions in the selected model based on a refined two-step spline estimator. We also discuss how to choose the tuning parameters. To estimate the standard deviation of the functional estimator, we adopt the smoothed bootstrap method. We conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze an obesity data set from a genome-wide association study as an illustration.