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Universal Local Linear Kernel Estimators in Nonparametric Regression

Author

Listed:
  • Yuliana Linke

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia)

  • Igor Borisov

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia)

  • Pavel Ruzankin

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia)

  • Vladimir Kutsenko

    (Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
    Department of Epidemiology of Noncommunicable Diseases, National Medical Research Center for Therapy and Preventive Medicine, 101990 Moscow, Russia)

  • Elena Yarovaya

    (Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
    Department of Epidemiology of Noncommunicable Diseases, National Medical Research Center for Therapy and Preventive Medicine, 101990 Moscow, Russia)

  • Svetlana Shalnova

    (Department of Epidemiology of Noncommunicable Diseases, National Medical Research Center for Therapy and Preventive Medicine, 101990 Moscow, Russia)

Abstract

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological cross-sectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2693-:d:875842
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    References listed on IDEAS

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