Partially functional linear regression in high dimensions

• 成果类型: Article
• 署名作者: Kong, Dehan; Xue, Kaijie; Yao, Fang; Zhang, Hao H.
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of Toronto; University of Arizona
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv062
• 发表日期: 2016
• 页码: 147159
• 关键词: nonconcave penalized likelihood; air-pollution; mortality; models; selection; cities

摘要

In modern experiments, functional and nonfunctional data are often encountered simultaneously when observations are sampled from random processes and high-dimensional scalar covariates. It is difficult to apply existing methods for model selection and estimation. We propose a new class of partially functional linear models to characterize the regression between a scalar response and covariates of both functional and scalar types. The new approach provides a unified and flexible framework that simultaneously takes into account multiple functional and ultrahigh-dimensional scalar predictors, enables us to identify important features, and offers improved interpretability of the estimators. The underlying processes of the functional predictors are considered to be infinite-dimensional, and one of our contributions is to characterize the effects of regularization on the resulting estimators. We establish the consistency and oracle properties of the proposed method under mild conditions, demonstrate its performance with simulation studies, and illustrate its application using air pollution data.