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An iterative plug-in algorithm for P-Spline regression

Author

Listed:
  • Sebastian Letmathe

    (Paderborn University)

  • Yuanhua Feng

    (Paderborn University)

Abstract

This paper proposes a new IPI- (iterative plug-in) rule for optimal smoothing for penalised splines with truncated polynomials. The IPI is based on a closed-form approximation to the optimal smoothing parameter. In contrast to a DPI- (direct plug-in) approach the current algorithm is fully automatic and self-contained. Our proposal is a fixpoint-search procedure and the resulting smoothing parameter is (theoretically) independent of the initial value. Like the DPI, the IPI-rule can be employed as a refining stage in order to improve the quality of other selection methods, e.g. Mallow’s Cp, Cross Validation or Residual Maximum Likelihood. Some numerical features of P-Splines as well as the performance of the IPI-algorithm are examined in detail through a simulation study. Our results reveal that our proposal works very well. Practical relevance of the IPI is illustrated by different data examples.

Suggested Citation

  • Sebastian Letmathe & Yuanhua Feng, 2022. "An iterative plug-in algorithm for P-Spline regression," Working Papers CIE 151, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:151
    as

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    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/ciepap/WP151.pdf
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    References listed on IDEAS

    as
    1. Yuanhua Feng & Jan Beran, 2013. "Optimal convergence rates in non-parametric regression with fractional time series errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 30-39, January.
    2. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
    3. Katsiaryna Schwarz & Tatyana Krivobokova, 2016. "A unified framework for spline estimators," Biometrika, Biometrika Trust, vol. 103(1), pages 121-131.
    4. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Sebastian Letmathe, 2022. "Data-driven P-Splines under short-range dependence," Working Papers CIE 152, Paderborn University, CIE Center for International Economics.

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    More about this item

    Keywords

    P-Splines; smoothing parameter; iterative plug-in; simulation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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