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Universal weighted kernel-type estimators for some class of regression models

Author

Listed:
  • Igor S. Borisov

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

  • Yuliana Yu. Linke

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

  • Pavel S. Ruzankin

    (Sobolev Institute of Mathematics
    Novosibirsk State University)

Abstract

For a wide class of nonparametric regression models with random design, we suggest consistent weighted least square estimators, asymptotic properties of which do not depend on correlation of the design points. In contrast to the predecessors’ results, the design is not required to be fixed or to consist of independent or weakly dependent random variables under the classical stationarity or ergodicity conditions; the only requirement being that the maximal spacing statistic of the design tends to zero almost surely (a.s.). Explicit upper bounds are obtained for the rate of uniform convergence in probability of these estimators to an unknown estimated random function which is assumed to lie in a Hölder space a.s. A Wiener process is considered as an example of such a random regression function. In the case of i.i.d. design points, we compare our estimators with the Nadaraya–Watson ones.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:2:d:10.1007_s00184-020-00768-0
    DOI: 10.1007/s00184-020-00768-0
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    References listed on IDEAS

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    Cited by:

    1. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    2. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2024. "Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency," Mathematics, MDPI, vol. 12(12), pages 1-23, June.

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