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Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments


  • Hertel, Ida
  • Kohler, Michael


A Monte Carlo method for estimation of the optimal design of a nonlinear parametric regression problem is presented. The basic idea is to use Monte Carlo to produce values of the error of a parametric regression estimate for randomly chosen designs and randomly chosen parameters; then, using this data, nonparametric regression is used to estimate the design for which the maximal expected error with respect to all possible parameter values is minimal. A theoretical result concerning the consistency of the optimal design estimate is presented, and the method is used to find an optimal design for an experimental fatigue test.

Suggested Citation

  • Hertel, Ida & Kohler, Michael, 2013. "Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 1-12.
  • Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:1-12 DOI: 10.1016/j.csda.2012.09.014

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    References listed on IDEAS

    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. Michael Kohler & Adam Krzyżak & Harro Walk, 2003. "Strong consistency of automatic kernel regression estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 287-308, June.
    3. Kohler, Michael & Krzyzak, Adam & Walk, Harro, 2011. "Estimation of the essential supremum of a regression function," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 685-693, June.
    4. Angelis, L. & Bora-Senta, E. & Moyssiadis, C., 2001. "Optimal exact experimental designs with correlated errors through a simulated annealing algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 275-296, September.
    5. Kohler, Michael & Krzyżak, Adam, 2012. "Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1566-1580.
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    Cited by:

    1. Diaz-Emparanza, Ignacio, 2014. "Numerical distribution functions for seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 237-247.
    2. Kohler, Michael & Krzyżak, Adam, 2015. "Estimation of a jump point in random design regression," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 247-255.


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