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Int Stat Rev. 2017 Aug;85(2):228-249. doi: 10.1111/insr.12163. Epub 2016 Feb 23.

Methods for scalar-on-function regression.

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Department of Child and Adolescent Psychiatry and Department of Population Health, New York University School of Medicine.
Department of Statistics, University of Haifa.
Department of Biostatistics, Columbia University Mailman School of Public Health.
Research School of Finance, Actuarial Studies and Statistics, Australian National University.
New York State Psychiatric Institute.


Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. 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, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.


functional additive model; functional generalized linear model; functional linear model; functional polynomial regression; functional single-index model; nonparametric functional regression

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