期刊
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
卷 76, 期 3, 页码 581-603出版社
OXFORD UNIV PRESS
DOI: 10.1111/rssb.12036
关键词
Principal components; Reproducing kernel Hilbert space; Additive models; Component selection; Functional data analysis; Smoothing spline
资金
- Natural Sciences and Engineering Research Council, Canada
- US National Institutes of Health [R01 CA-085848]
- National Science Foundation [DMS-0645293]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1347844] Funding Source: National Science Foundation
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.
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