Time-Varying Additive Models for Longitudinal Data

• 成果类型: Article
• 署名作者: Zhang, Xiaoke; Park, Byeong U.; Wang, Jane-Ling
• 署名单位: University of California System; University of California Davis; Seoul National University (SNU)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.778776
• 发表日期: 2013
• 页码: 983-998
• 关键词: Nonparametric regression; asymptotic properties; efficient estimation; components

摘要

The additive model is an effective dimension-reduction approach that also provides flexibility in modeling the relation between a response variable and key covariates. The literature is largely developed to scalar response and vector covariates. In this article, more complex data are of interest, where both the response and the covariates are functions. We propose a functional additive model together with a new backfitting algorithm to estimate the unknown regression functions, whose components are time-dependent additive functions of the covariates. Such functional data may not be completely observed since measurements may only be collected intermittently at discrete time points. We develop a unified platform and an efficient approach that can cover both dense and sparse functional data and the needed theory for statistical inference. We also establish the oracle properties of the proposed estimators of the component functions.