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On general bootstrap of empirical estimator of a semi-Markov kernel with applications

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  • Bouzebda, Salim
  • Limnios, Nikolaos

Abstract

The aim of this paper is to introduce a general bootstrap by exchangeable weight random variables for empirical estimators of the semi-Markov kernels and of the conditional transition probabilities for semi-Markov processes with countable state space. Asymptotic properties of these generalized bootstrapped empirical distributions are obtained by a martingale approach. We show how to apply our results to the construction of confidence intervals and change point problem where the limiting distribution of the proposed statistic is derived under the null hypothesis.

Suggested Citation

  • Bouzebda, Salim & Limnios, Nikolaos, 2013. "On general bootstrap of empirical estimator of a semi-Markov kernel with applications," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 52-62.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:52-62
    DOI: 10.1016/j.jmva.2012.11.008
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    References listed on IDEAS

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    1. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    2. Pierre Combris & Patrice Bertail & Christine Boizot-Szantai & Jean-Claude Poupa, 1995. "La consommation alimentaire en 1991 : distribution des quantités consommées à domicile," Post-Print hal-01931697, HAL.
    3. Csörgő Miklós & Horváth Lajos & Szyszkowicz Barbara, 1997. "Integral Tests For Suprema Of Kiefer Processes With Application," Statistics & Risk Modeling, De Gruyter, vol. 15(4), pages 365-378, April.
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    Cited by:

    1. Salim Bouzebda & Issam Elhattab & Anouar Abdeldjaoued Ferfache, 2022. "General M-Estimator Processes and their m out of n Bootstrap with Functional Nuisance Parameters," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2961-3005, December.
    2. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    3. Salim Bouzebda & Chrysanthi Papamichail & Nikolaos Limnios, 2018. "On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 49-86, January.
    4. Irene Votsi & Salim Bouzebda, 2025. "Bootstrap of Reliability Indicators for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-18, March.

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