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Estimating the smoothing parameter in generalized spline-based regression

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  • Angelika Linde

    (University of Bremen)

Abstract

Summary Smoothing with splines requires a smoothing parameter which is most often obtained by cross-validation. Interpreting splines from a Bayesian point of view this is an empirical Bayesian approach. A fully Bayesian approach with a (hyper-) prior for the smoothing parameter is computationally more demanding even for Gaussian data and really accessible only using simulation methods. Smoothing in generalized regression models is presented in a Bayesian interpretation and tried with Gaussian and binary data using the implementation of Gibbs sampling in BUGS. The results are compared to those obtained by cross-validation. The approach essentially does work but convergence of just the smoothing parameter turns out to be crucial. The sensitivity of the estimated function values w.r.t. to the prior is satisfactory.

Suggested Citation

  • Angelika Linde, 2001. "Estimating the smoothing parameter in generalized spline-based regression," Computational Statistics, Springer, vol. 16(1), pages 73-95, March.
    • Handle: RePEc:spr:compst:v:16:y:2001:i:1:d:10.1007_s001800100052
    DOI: 10.1007/s001800100052
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    References listed on IDEAS

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    1. Linde Angelika van der, 1993. "A Note On Smoothing Splines As Bayesian Estimates," Statistics & Risk Modeling, De Gruyter, vol. 11(1), pages 61-68, January.
    2. A. Linde, 1995. "Splines from a Bayesian point of view," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 63-81, June.
    3. Kay, Jim, 1992. "Asymptotic comparison factors for smoothing parameter choices in regression problems," Statistics & Probability Letters, Elsevier, vol. 15(4), pages 329-335, November.
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    Cited by:

    1. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.

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    1. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.

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