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Smoothing parameter selection for a class of semiparametric linear models
Author(s) -
Reiss Philip T.,
Todd Ogden R.
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00695.x
Subject(s) - smoothing , semiparametric regression , semiparametric model , mathematics , parametric statistics , scalar (mathematics) , model selection , selection (genetic algorithm) , estimating equations , regression , spline (mechanical) , principal component analysis , functional principal component analysis , regression analysis , functional data analysis , smoothing spline , parametric model , statistics , computer science , maximum likelihood , artificial intelligence , engineering , geometry , structural engineering , bilinear interpolation , spline interpolation
Summary. Spline‐based approaches to non‐parametric 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 component regression, a method for regressing scalars on functions, to two chemometric data sets.