Structured functional additive regression in reproducing kernel Hilbert spaces

• 成果类型: Article
• 署名作者: Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen
• 署名单位: Virginia Polytechnic Institute & State University; University of Toronto; University of Arizona
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12036
• 发表日期: 2014
• 页码: 581-603
• 关键词: linear-models; selection

摘要

Functional additive models provide a flexible yet simple framework for regressions involving functional predictors. The utilization of a data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting non-linear additive components has been less studied. In this work, we propose a new regularization framework for structure estimation in the context of reproducing kernel Hilbert spaces. The approach proposed takes advantage of functional principal components which greatly facilitates implementation and theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.