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Model selection in spline nonparametric regression

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  • Sally Wood
  • Robert Kohn
  • Tom Shively
  • Wenxin Jiang

Abstract

A Bayesian approach is presented for model selection in nonparametric regression with Gaussian errors and in binary nonparametric regression. A smoothness prior is assumed for each component of the model and the posterior probabilities of the candidate models are approximated using the Bayesian information criterion. We study the model selection method by simulation and show that it has excellent frequentist properties and gives improved estimates of the regression surface. All the computations are carried out efficiently using the Gibbs sampler.

Suggested Citation

  • Sally Wood & Robert Kohn & Tom Shively & Wenxin Jiang, 2002. "Model selection in spline nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 119-139, January.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:1:p:119-139
    DOI: 10.1111/1467-9868.00328
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    Cited by:

    1. Samiran Sinha & Bani K. Mallick & Victor Kipnis & Raymond J. Carroll, 2010. "Semiparametric Bayesian Analysis of Nutritional Epidemiology Data in the Presence of Measurement Error," Biometrics, The International Biometric Society, vol. 66(2), pages 444-454, June.
    2. Cheng, Chin-I. & Speckman, Paul L., 2012. "Bayesian smoothing spline analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3945-3958.
    3. Dongchu Sun & Paul Speckman, 2008. "Bayesian hierarchical linear mixed models for additive smoothing splines," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 499-517, September.
    4. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    5. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    6. McKay Curtis, S. & Banerjee, Sayantan & Ghosal, Subhashis, 2014. "Fast Bayesian model assessment for nonparametric additive regression," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 347-358.

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