Methods for scalar-on-function regression

Philip T. Reiss, Jeff Goldsmith, Han Lin Shang, R. Todd Ogden

Research output: Contribution to journalArticlepeer-review


Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images and so on are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorising the basic model types as linear, non-linear and non-parametric. We discuss publicly available software packages and illustrate some of the procedures by application to a functional magnetic resonance imaging data set.

Original languageEnglish
Pages (from-to)228-249
Number of pages22
JournalInternational Statistical Review
Issue number2
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2016 The Authors and International Statistical Institute.


  • Functional additive model
  • Functional generalised linear model
  • Functional linear model
  • Functional polynomial regression
  • Functional single-index model
  • Non-parametric functional regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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