Penalized function-on-function regression

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

Research output: Contribution to journalArticle

31 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)539-568
Number of pages30
JournalComputational Statistics
Volume30
Issue number2
DOIs
StatePublished - 12 Jun 2015

Fingerprint

Functional Response
Regression Function
Mixed Model
Predictors
Diffusion tensor imaging
Penalized Regression
Sparse Grids
Categorical
Expand
Byproducts
Confidence interval
Covariates
Brain
Tensor
Regression
Imaging
Scenarios
Software
Mixed model

Keywords

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

Cite this

Ivanescu, Andrada ; Staicu, Ana Maria ; Scheipl, Fabian ; Greven, Sonja. / Penalized function-on-function regression. In: Computational Statistics. 2015 ; Vol. 30, No. 2. pp. 539-568.
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Ivanescu, A, Staicu, AM, Scheipl, F & Greven, S 2015, 'Penalized function-on-function regression', Computational Statistics, vol. 30, no. 2, pp. 539-568. https://doi.org/10.1007/s00180-014-0548-4

Penalized function-on-function regression. / Ivanescu, Andrada; Staicu, Ana Maria; Scheipl, Fabian; Greven, Sonja.

In: Computational Statistics, Vol. 30, No. 2, 12.06.2015, p. 539-568.

Research output: Contribution to journalArticle

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