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Theory for penalised spline regression

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  • Peter Hall
  • J. D. Opsomer
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    Abstract

    Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to achieve the optimal nonparametric convergence rateestablished by Stone (1982). Copyright 2005, Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.105
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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 92 (2005)
    Issue (Month): 1 (March)
    Pages: 105-118

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    Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:105-118

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    Cited by:
    1. Haiqiang Chen & Ying Fang & Yingxing Li, 2013. "Estimation and Inference for Varying-coefficient Models with Nonstationary Regressors using Penalized Splines," SFB 649 Discussion Papers SFB649DP2013-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Schluter, Christian & Wahba, Jackline, 2009. "Illegal Migration, Wages, and Remittances: Semi-Parametric Estimation of Illegality Effects," IZA Discussion Papers 4527, Institute for the Study of Labor (IZA).
    3. repec:wyi:journl:002195 is not listed on IDEAS
    4. Christian Schluter & Jackline Wahba, 2012. "Abstract: Illegal Migration, Wages, and Remittances: Semi-Parametric Estimation of Illegality Effects," Norface Discussion Paper Series 2012037, Norface Research Programme on Migration, Department of Economics, University College London.
    5. Sima, Diana M. & Van Huffel, Sabine, 2006. "A class of template splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3486-3499, August.
    6. Wahba, Jackline & Schluter, Christian, 2009. "Illegal migration, wages and remittances- semi-parametric estimation of illegality effects," Discussion Paper Series In Economics And Econometrics 0913, Economics Division, School of Social Sciences, University of Southampton.

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