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Fixed-design regression estimation based on real and artificial data

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  • Dmytro Furer
  • Michael Kohler
  • Adam Krzyżak

Abstract

In this article, we study the fixed-design regression estimation based on real and artificial data, where the artificial data comes from previously undertaken similar experiments. A least-squares estimate that gives different weights to the real and artificial data is introduced. It is investigated under which condition the rate of convergence of this estimate is better than the rate of convergence of an ordinary least-squares estimate applied to the real data only. The results are illustrated using simulated and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:223-241
    DOI: 10.1080/10485252.2012.749257
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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.
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    Cited by:

    1. 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.
    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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