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Multiparameter Bandwidth Processes and Adaptive Surface Smoothing

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  • Muller, H. G.
  • Prewitt, K. A.

Abstract

We derive a functional limit theorem for a sequence of bandwidth processes with multivariate time and show that the limit process is multivariate Gaussian. This theorem is then applied to show asymptotic efficiency of certain data-adaptive local bandwidth choices for kernel estimators of multivariate regression functions and their derivatives. The cases where optimal multivariate bandwidths exist as minimizers of leading mean squared error terms are characterized.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:47:y:1993:i:1:p:1-21
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    Cited by:

    1. 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.
    2. 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.
    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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