IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v87y2003i1p191-217.html
   My bibliography  Save this article

Nonparametric estimation of the location of a maximum in a response surface

Author

Listed:
  • Facer, Matthew R.
  • Müller, Hans-Georg

Abstract

We explore a nonparametric version of response surface analysis. Estimates for the location where maximum response occurs are proposed and their asymptotic distribution is investigated. The proposed estimates are based on kernel and local least squares methods. We construct asymptotic confidence regions for the location and include comparisons with the quadratic response surface approach. The methods are illustrated for the two-dimensional case with AIDS incidence data, where the point of maximum incidence is of interest.

Suggested Citation

  • Facer, Matthew R. & Müller, Hans-Georg, 2003. "Nonparametric estimation of the location of a maximum in a response surface," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 191-217, October.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:1:p:191-217
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00030-7
    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

    as
    1. Chen, Hung & Huang, Mong-Na Lo & Huang, Wen-Jang, 1996. "Estimation of the Location of the Maximum of a Regression Function Using Extreme Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 191-214, May.
    2. Muller, H. G. & Prewitt, K. A., 1993. "Multiparameter Bandwidth Processes and Adaptive Surface Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 1-21, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Promit Ghosal & Bodhisattva Sen, 2017. "On Univariate Convex Regression," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 215-253, August.
    2. Ciuperca Gabriela, 2004. "Maximum likelihood estimator in a two-phase nonlinear random regression model," Statistics & Risk Modeling, De Gruyter, vol. 22(4/2004), pages 335-349, April.
    3. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bai, Zhidong & Chen, Zehua & Wu, Yaohua, 2003. "Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 319-334, February.
    2. V. Bartkutė & L. Sakalauskas, 2009. "Statistical Inferences for Termination of Markov Type Random Search Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 475-493, June.
    3. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.
    4. Carlos A. Flores, 2007. "Estimation of Dose-Response Functions and Optimal Doses with a Continuous Treatment," Working Papers 0707, University of Miami, Department of Economics.
    5. Cristóbal, J. A. & Alcalá, J. T., 1998. "Error Process Indexed by Bandwidth Matrices in Multivariate Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 207-236, August.

    Corrections

    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:jmvana:v:87:y:2003:i:1:p:191-217. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.