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Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces

Author

Listed:
  • Michel Harel

    (Institut de Mathématiques de Toulouse
    Université de Limoges)

  • Joseph Ngatchou-Wandji

    (EHESP Rennes & Institut Élie Cartan de Lorraine)

  • Livasoa Andriamampionona

    (University of Antananarivo)

  • Victor Harison

    (University of Antananarivo)

Abstract

This paper deals with the weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces. It is an extension of Harel et al. (J Math Anal Appl 189:240–255, 1995) from the one-dimensional case to the multivariate and multidimensional case. The estimators are based on a sequence of non-negative independent and identically distributed (iid) random vectors. They are expressed as infinite sums of k-folds convolutions of the empirical distribution function. Their weak convergence study heavily rests on that of the empirical distribution function.

Suggested Citation

  • Michel Harel & Joseph Ngatchou-Wandji & Livasoa Andriamampionona & Victor Harison, 2022. "Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 485-504, October.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:3:d:10.1007_s11203-021-09263-3
    DOI: 10.1007/s11203-021-09263-3
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    References listed on IDEAS

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    1. Edward W. Frees, 1986. "Warranty analysis and renewal function estimation," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(3), pages 361-372, August.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    3. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(2), pages 210-230, August.
    4. Frees, Edward W, 1988. "Estimating the Cost of a Warranty," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 79-86, January.
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