Computational Statistics

, Volume 30, Issue 2, pp 539–568 | Cite as

Penalized function-on-function regression

  • Andrada E. Ivanescu
  • Ana-Maria Staicu
  • Fabian Scheipl
  • Sonja Greven
Original Paper

Abstract

A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed on the same or different domains than the functional response, on a dense or sparse grid, and with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the mixed model inference. The proposed methods are accompanied by easy to use and robust software implemented in the pffr function of the R package refund. Methodological developments are general, but were inspired by and applied to a diffusion tensor imaging brain tractography dataset.

Keywords

Functional data analysis Functional regression model  Mixed model Multiple functional predictors Penalized splines Tractography data 

Supplementary material

180_2014_548_MOESM1_ESM.pdf (2.3 mb)
Supplementary material 1 (pdf 2377 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrada E. Ivanescu
    • 1
  • Ana-Maria Staicu
    • 2
  • Fabian Scheipl
    • 3
  • Sonja Greven
    • 3
  1. 1.Department of Mathematical SciencesMontclair State UniversityMontclairUSA
  2. 2.Department of StatisticsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of StatisticsLudwig-Maximilians-University MunichMunichGermany

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