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A Comparison of Regression Spline Smoothing Procedures

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  • M. P. Wand

    (Harvard University)

Abstract

Summary Regression spline smoothing involves modelling a regression function as a piecewise polynomial with a high number of pieces relative to the sample size. Because the number of possible models is so large, efficient strategies for choosing among them are required. In this paper we review approaches to this problem and compare them through a simulation study. For simplicity and conciseness we restrict attention to the univariate smoothing setting with Gaussian noise and the truncated polynomial regression spline basis.

Suggested Citation

  • M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    • Handle: RePEc:spr:compst:v:15:y:2000:i:4:d:10.1007_s001800000047
    DOI: 10.1007/s001800000047
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    References listed on IDEAS

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    1. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    2. D. G. T. Denison & B. K. Mallick & A. F. M. Smith, 1998. "Automatic Bayesian curve fitting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 333-350.
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    Cited by:

    1. Jang, Dongik & Oh, Hee-Seok, 2011. "Enhancement of spatially adaptive smoothing splines via parameterization of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1029-1040, February.
    2. Cao, Jiguo & Ramsay, James O., 2009. "Generalized profiling estimation for global and adaptive penalized spline smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2550-2562, May.
    3. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    4. Lee, Thomas C. M., 2003. "Smoothing parameter selection for smoothing splines: a simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 139-148, February.
    5. Men, Tianli & Li, Yan-Fu & Ji, Yujun & Zhang, Xinliang & Liu, Pengfei, 2022. "Health assessment of high-speed train wheels based on group-profile data," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    6. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    7. Soumya D. Mohanty & Ethan Fahnestock, 2021. "Adaptive spline fitting with particle swarm optimization," Computational Statistics, Springer, vol. 36(1), pages 155-191, March.
    8. Hervé Cardot, 2002. "Local roughness penalties for regression splines," Computational Statistics, Springer, vol. 17(1), pages 89-102, March.
    9. Leitenstorfer, Florian & Tutz, Gerhard, 2007. "Knot selection by boosting techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4605-4621, May.
    10. Gerhard Tutz & Harald Binder, 2006. "Generalized Additive Modeling with Implicit Variable Selection by Likelihood-Based Boosting," Biometrics, The International Biometric Society, vol. 62(4), pages 961-971, December.
    11. Annie Qu & Runze Li, 2006. "Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(2), pages 379-391, June.
    12. Robert Mohr & Maximilian Coblenz & Peter Kirst, 2023. "Globally optimal univariate spline approximations," Computational Optimization and Applications, Springer, vol. 85(2), pages 409-439, June.
    13. Ciprian Crainiceanu & David Ruppert & Raymond Carroll, 2004. "Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1061, Berkeley Electronic Press.
    14. Kagerer, Kathrin, 2013. "A short introduction to splines in least squares regression analysis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 472, University of Regensburg, Department of Economics.
    15. Carlos E. Melo & Oscar O. Melo & Jorge Mateu, 2018. "A distance-based model for spatial prediction using radial basis functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 263-288, April.
    16. Goepp, Vivien & Bouaziz, Olivier & Nuel, Grégory, 2025. "Spline regression with automatic knot selection," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
    17. Gerhard Tutz, 2022. "Item Response Thresholds Models: A General Class of Models for Varying Types of Items," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1238-1269, December.
    18. Maximilian Osterhaus, 2024. "A Sparse Grid Approach for the Nonparametric Estimation of High-Dimensional Random Coefficient Models," Papers 2408.07185, arXiv.org.
    19. Nielsen, J.D. & Dean, C.B., 2008. "Adaptive functional mixed NHPP models for the analysis of recurrent event panel data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3670-3685, March.

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