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Smoothing parameter selection for a class of semiparametric linear models. (English) Zbl 1248.62057
Summary: Spline-based approaches to nonparametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results which are common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal components regression, a method for regressing scalars on functions, to two chemometric data sets.

MSC:
62G08 Nonparametric regression and quantile regression
62H25 Factor analysis and principal components; correspondence analysis
65D07 Numerical computation using splines
62J05 Linear regression; mixed models
Software:
SemiPar
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