Penalized function-on-function regression

Andrada E. Ivanescu, Ana Maria Staicu, Fabian Scheipl, Sonja Greven

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


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.

Original languageEnglish
Pages (from-to)539-568
Number of pages30
JournalComputational Statistics
Issue number2
StatePublished - 12 Jun 2015


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


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