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Smoothing spline regression estimation based on real and artificial data

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  • Dmytro Furer
  • Michael Kohler

Abstract

In this article we introduce a smoothing spline estimate for fixed design regression estimation based on real and artificial data, where the artificial data comes from previously undertaken similar experiments. The smoothing spline estimate gives different weights to the real and the artificial data. It is investigated under which conditions the rate of convergence of this estimate is better than the rate of convergence of the ordinary smoothing spline estimate applied to the real data only. The finite sample size performance of the estimate is analyzed using simulated data. The usefulness of the estimate is illustrated by applying it in the context of experimental fatigue tests. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Dmytro Furer & Michael Kohler, 2015. "Smoothing spline regression estimation based on real and artificial data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 711-746, August.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:6:p:711-746
    DOI: 10.1007/s00184-014-0524-6
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    References listed on IDEAS

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    1. Zhao, L. C., 1987. "Exponential bounds of mean error for the nearest neighbor estimates of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 168-178, February.
    2. Dmytro Furer & Michael Kohler & Adam Krzyżak, 2013. "Fixed-design regression estimation based on real and artificial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 223-241, March.
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    Cited by:

    1. Ann-Kathrin Bott & Michael Kohler, 2017. "Nonparametric estimation of a conditional density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 189-214, February.
    2. Matthias Hansmann & Benjamin M. Horn & Michael Kohler & Stefan Ulbrich, 2022. "Estimation of conditional distribution functions from data with additional errors applied to shape optimization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 323-343, April.

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