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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    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), 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.

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