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Methods for scalar-on-function regression.

Philip T Reiss1,2, Jeff Goldsmith3, Han Lin Shang4

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Summary
This summary is machine-generated.

Functional data analysis (FDA) models curves and spectra as data units. This review covers linear, nonlinear, and nonparametric regression methods for scalar responses with functional predictors, including software and an fMRI example.

Keywords:
functional additive modelfunctional generalized linear modelfunctional linear modelfunctional polynomial regressionfunctional single-index modelnonparametric functional regression

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Machine Learning

Background:

  • Functional Data Analysis (FDA) treats curves, spectra, and images as fundamental data units.
  • A key challenge in FDA is developing regression models with scalar outcomes and functional predictors.

Purpose of the Study:

  • To review major approaches for fitting regression models in functional data analysis.
  • To categorize models into linear, nonlinear, and nonparametric types.
  • To discuss available software and demonstrate applications using functional magnetic resonance imaging (fMRI) data.

Main Methods:

  • Categorization of regression models into linear, nonlinear, and nonparametric frameworks.
  • Review of established and emerging methodologies within each category.
  • Application of selected methods to a real-world functional magnetic resonance imaging (fMRI) dataset.

Main Results:

  • Comprehensive overview of diverse regression modeling strategies in FDA.
  • Demonstration of practical implementation and utility of FDA methods.
  • Highlighting the applicability of FDA in analyzing complex data like fMRI.

Conclusions:

  • The field of functional data analysis offers robust methods for regression with functional predictors.
  • Linear, nonlinear, and nonparametric approaches provide a flexible toolkit for various data types.
  • Available software facilitates the application of these advanced statistical techniques.