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