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

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  • Hertel, Ida
  • Kohler, Michael

Abstract

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

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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. 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.
    3. 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.
    4. 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.
    5. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    6. 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.
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    Cited by:

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    2. Khakifirooz, Marzieh & Fathi, Michel & Lee, I-Chen & Tseng, Sheng-Tsaing, 2023. "Neural ordinary differential equation for sequential optimal design of fatigue test under accelerated life test analysis," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    3. 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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