Smoothing parameter selection for a class of semiparametric linear models

Philip T. Reiss and R. Todd Ogden

Journal Of The Royal Statistical Society Series B, 2009, vol. 71, issue 2, pages 505-523

Abstract: 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. Copyright (c) 2009 Royal Statistical Society.

Date: 2009

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