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Applied Statistics

Selected Works

Functional linear model

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Full-Text Articles in Physical Sciences and Mathematics

Methods For Scalar-On-Function Regression, Philip T. Reiss, Jeff Goldsmith, Han Lin Shang, R. Todd Ogden Jul 2017

Methods For Scalar-On-Function Regression, Philip T. Reiss, Jeff Goldsmith, Han Lin Shang, R. Todd Ogden

Philip T. Reiss

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.

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Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes Dec 2009

Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes

Lei Huang

Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals …

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Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes Dec 2009

Fast Function-On-Scalar Regression With Penalized Basis Expansions, Philip T. Reiss, Lei Huang, Maarten Mennes

Philip T. Reiss

Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals …

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