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Matematicheskie Zametki, 2023, Volume 114, Issue 3, Pages 353–369
DOI: https://doi.org/10.4213/mzm13906 (Mi mzm13906) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators

Yu. Yu. Linke

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (699 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm13906
Abstract: The consistency of classical local linear kernel estimators in nonparametric regression is proved under constraints on design elements (regressors) weaker than those known earlier. The obtained conditions are universal with respect to the stochastic nature of design, which may be both fixed regular and random and is not required to consist of independent or weakly dependent random variables. Sufficient conditions for pointwise and uniform consistency of classical local linear estimators are stated in terms of the asymptotic behavior of the number of design elements in certain neighborhoods of points in the domain of the regression function.
Keywords: nonparametric regression, local linear estimator, uniform consistency, fixed design, random design, highly dependent design elements.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0015
This work was supported by the Program of fundamental scientific studies of the Siberian Branch of the Russian Academy of Sciences (grant no. FWNF-2022-0015).
Received: 29.01.2023
Revised: 21.02.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 3, Pages 308–321
DOI: https://doi.org/10.1134/S0001434623090043
Bibliographic databases:
Document Type: Article
UDC: 519.234
MSC: 519.234
Language: Russian
Citation: Yu. Yu. Linke, “On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators”, Mat. Zametki, 114:3 (2023), 353–369; Math. Notes, 114:3 (2023), 308–321
Citation in format AMSBIB
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\paper On Sufficient Conditions for the Consistency of Local Linear Kernel Estimators
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\pages 353--369
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\jour Math. Notes
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  • https://doi.org/10.4213/mzm13906
  • https://www.mathnet.ru/eng/mzm/v114/i3/p353
    • This publication is cited in the following 1 articles:
    1. Yuliana Linke, Igor Borisov, Pavel Ruzankin, Vladimir Kutsenko, Elena Yarovaya, Svetlana Shalnova, “Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency”, Mathematics, 12:12 (2024), 1890  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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