IDEAS home Printed from
   My bibliography  Save this article

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

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. 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.
    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. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

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


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:1-12. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.