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Local roughness penalties for regression splines

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  • Hervé Cardot

    (INRA Toulouse)

Abstract

Summary This paper introduces a new nonparametric estimator of the regression based on penalized regression splines. Local roughness penalties that rely on local support properties of B-splines are introduced in order to deal with the spatial heterogeneity of the function to be estimated. This estimator is shown to attain optimal rates of convergence. Then its good performances are confirmed on a simulation study.

Suggested Citation

  • Hervé Cardot, 2002. "Local roughness penalties for regression splines," Computational Statistics, Springer, vol. 17(1), pages 89-102, March.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:1:d:10.1007_s001800200092
    DOI: 10.1007/s001800200092
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    References listed on IDEAS

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    1. Diack, C.A.T. & Thomas-Agnan, C., 1996. "A Nonparametric Test of The Non-Convexity of Regression," Papers 976.427, Toulouse - GREMAQ.
    2. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    3. 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.
    4. Besse, Philippe C. & Cardot, Herve & Ferraty, Frederic, 1997. "Simultaneous non-parametric regressions of unbalanced longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 255-270, May.
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    Cited by:

    1. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503, April.

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