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Adaptive nonparametric estimation of a multivariate regression function

Author

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  • Mack, Y.P.
  • Mu¨ller, Hans-Georg

Abstract

We consider the kernel estimation of a multivariate regression function at a point. Theoretical choices of the bandwidth are possible for attaining minimum mean squared error or for local scaling, in the sense of asymptotic distribution. However, these choices are not available in practice. We follow the approach of Krieger and Pickands (Ann. Statist.9 (1981) 1066-1078) and Abramson (J. Multivariate Anal.12 (1982), 562-567) in constructing adaptive estimates after demonstrating the weak convergence of some error process. As consequences, efficient data-driven consistent estimation is feasible, and data-driven local scaling is also feasible. In the latter instance, nearest-neighbor-type estimates and variance-stabilizing estimates are obtained as special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:23:y:1987:i:2:p:169-183
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    Citations

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    Cited by:

    1. Miroslaw Pawlak, 1991. "On the almost everywhere properties of the kernel regression estimate," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 311-326, June.
    2. Robinson, P. M., 1995. "The approximate distribution of nonparametric regression estimates," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 193-201, May.
    3. 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.
    4. Igor S. Borisov & Yuliana Yu. Linke & Pavel S. Ruzankin, 2021. "Universal weighted kernel-type estimators for some class of regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 141-166, February.

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