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Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields

Author

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  • Livasoa Andriamampionona

    (Department of Mathematics and Informatics, University of Antananarivo, Antananarivo 101, Madagascar)

  • Victor Harison

    (Department of Mathematics and Informatics, University of Antananarivo, Antananarivo 101, Madagascar)

  • Michel Harel

    (INSPÉ de Limoges, Université de Limoges, 87036 Limoges, CEDEX 3, France
    Institut de Mathématiques de Toulouse, UMR5219 UPS, 31062 Toulouse, CEDEX 9, France
    Laboratoire Vie-Santé, UR 24 134, Faculté de Médecine, 87025 Limoges, France)

Abstract

In this paper, we study the asymptotic normality of a nonparametric estimator of the renewal function associated with a sequence of absolutely continuous nonnegative two-dimensional random fields. We prove that this estimator is asymptotically unbiased. The asymptotic normality of this estimator is established.

Suggested Citation

  • Livasoa Andriamampionona & Victor Harison & Michel Harel, 2023. "Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields," Mathematics, MDPI, vol. 11(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4048-:d:1246650
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    References listed on IDEAS

    as
    1. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.
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    Cited by:

    1. Livasoa Andriamampionona & Victor Harison & Michel Harel, 2024. "Non-Parametric Estimation of the Renewal Function for Multidimensional Random Fields," Mathematics, MDPI, vol. 12(12), pages 1-22, June.

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