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Asymptotic behavior of nonparametric estimators of the two-dimensional and bivariate renewal functions

Author

Listed:
  • Michel Harel

    (UMR5219 UPS
    Université de Limoges)

  • Livasoa Andriamampionona

    (University of Antananarivo)

  • Victor Harison

    (University of Antananarivo)

Abstract

We study the asymptotic behavior of the two-dimensional or bivariate nonparametric estimators of the renewal function associated to a sequence of absolutely continuous non-negative random vectors. We prove that these estimators are consistent and unbiased when the random vectors are independent and identically distributed but are neither consistent nor unbiased when the random vectors are strictly stationary absolutely regular. The asymptotic normality of these estimators on the space $$\mathbb {R}_{+}^{2}$$ R + 2 is established when the random vectors are independent and identically distributed.

Suggested Citation

  • Michel Harel & Livasoa Andriamampionona & Victor Harison, 2019. "Asymptotic behavior of nonparametric estimators of the two-dimensional and bivariate renewal functions," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 499-523, October.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:3:d:10.1007_s11203-018-9192-x
    DOI: 10.1007/s11203-018-9192-x
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    References listed on IDEAS

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    1. Joseph Ngatchou-Wandji & Michel Harel, 2013. "A Cramér-von Mises test for symmetry of the error distribution in asymptotically stationary stochastic models," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 207-236, October.
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