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Smoothing parameter selection for a class of semiparametric linear models

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  • Philip T. Reiss
  • R. Todd Ogden
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    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.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 71 (2009)
    Issue (Month): 2 ()
    Pages: 505-523

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    Handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:505-523

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    Cited by:
    1. Christian Schellhase & Göran Kauermann, 2012. "Density estimation and comparison with a penalized mixture approach," Computational Statistics, Springer, Springer, vol. 27(4), pages 757-777, December.
    2. Marra, Giampiero & Wood, Simon N., 2011. "Practical variable selection for generalized additive models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 55(7), pages 2372-2387, July.
    3. Tatyana Krivobokova, 2011. "Smoothing parameter selection in two frameworks for penalized splines," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 85, Courant Research Centre PEG, revised 18 Oct 2012.
    4. Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2012. "Bayesian Nonparametric Instrumental Variable Regression based on Penalized Splines and Dirichlet Process Mixtures," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 127, Courant Research Centre PEG.

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