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Cramér’s type results for some bootstrapped U-statistics

Author

Listed:
  • Sergio Alvarez-Andrade

    (Université de Technologie de Compiègne)

  • Salim Bouzebda

    (Université de Technologie de Compiègne)

Abstract

In the present paper, we are mainly interested in Cramér-type results for the weighted bootstrap of the U-statistics. The method of proof is based on the Hoeffding decomposition according to the bootstrapped Cramér transform together with the contraction technique. Finally, we investigate the U-statistics indexed by a one dimensional symmetric random walk.

Suggested Citation

  • Sergio Alvarez-Andrade & Salim Bouzebda, 2020. "Cramér’s type results for some bootstrapped U-statistics," Statistical Papers, Springer, vol. 61(4), pages 1685-1699, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-018-0999-8
    DOI: 10.1007/s00362-018-0999-8
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    References listed on IDEAS

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    1. Hall, Peter, 1990. "On the relative performance of bootstrap and Edgeworth approximations of a distribution function," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 108-129, October.
    2. M. Vandemaele & N. Veraverbeke, 1985. "Cramer type large deviations for studentized U-statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 165-179, December.
    3. Borovskikh, Yuri V. & Robinson, John, 2008. "Large deviations of bootstrapped U -statistics," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1793-1806, September.
    4. Serfling, Robert & Wang, Wenyang, 2000. "A large deviation theorem for U-processes," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 181-193, August.
    5. Dasgupta, Ratan, 2010. "Bootstrap of deviation probabilities with applications," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2137-2148, October.
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    Cited by:

    1. Inass Soukarieh & Salim Bouzebda, 2022. "Exchangeably Weighted Bootstraps of General Markov U -Process," Mathematics, MDPI, vol. 10(20), pages 1-42, October.

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