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Error Process Indexed by Bandwidth Matrices in Multivariate Local Linear Smoothing

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  • Cristóbal, J. A.
  • Alcalá, J. T.

Abstract

We focus on nonparametric multivariate regression function estimation by locally weighted least squares. The asymptotic behavior for a sequence of error processes indexed by bandwidth matrices is derived. We discuss feasible data-driven consistent estimators minimizing asymptotic mean squared error or efficient estimators reducing asymptotic bias at points where opposite sign curvatures of the regression function are present in different directions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:66:y:1998:i:2:p:207-236
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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. Abramson, Ian S., 1982. "Arbitrariness of the pilot estimator in adaptive kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 562-567, December.
    3. Mack, Y.P. & Mu¨ller, Hans-Georg, 1987. "Adaptive nonparametric estimation of a multivariate regression function," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 169-183, December.
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    Cited by:

    1. Perone Pacifico, M. & Genovese, C. & Verdinelli, I. & Wasserman, L., 2007. "Scan clustering: A false discovery approach," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1441-1469, August.

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