Structured functional additive regression in reproducing kernel Hilbert spaces

Hongxiao Zhu, Fang Yao, Hao Zhang

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)581-603
Number of pages23
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume76
Issue number3
DOIs
StatePublished - 2014

Fingerprint

Additive Functional
Reproducing Kernel Hilbert Space
Regression
Functional Linear Model
Penalized Least Squares
Additive Models
Functional Model
Principal Components
Data-driven
Penalty
Predictors
Theoretical Analysis
Regularization
Rate of Convergence
Simulation Study
Kernel
Hilbert space
Framework

Keywords

  • Additive models
  • Component selection
  • Functional data analysis
  • Principal components
  • Reproducing kernel hilbert space
  • Smoothing spline

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Structured functional additive regression in reproducing kernel Hilbert spaces. / Zhu, Hongxiao; Yao, Fang; Zhang, Hao.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 76, No. 3, 2014, p. 581-603.

Research output: Contribution to journalArticle

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