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Large deviations of bootstrapped U -statistics

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  • Borovskikh, Yuri V.
  • Robinson, John

Abstract

We develop large deviation results with Cramer's series and the best possible remainder term for bootstrapped U-statistics with non-degenerate bounded kernels. The method of the proof is based on the contraction technique of Keener, Robinson and Weber [R.W. Keener, J. Robinson, N.C. Weber, Tail probability approximations for U-statistics, Statist. Probab. Lett. 37 (1) (1998) 59-65], which is a natural generalization of the classical conjugate distribution technique due to Cramer [H. Cramer, Sur un nouveau théoréme-limite de la theorie des probabilites, Actual. Sci. Indust. 736 (1938) 5-23].

Suggested Citation

  • Borovskikh, Yuri V. & Robinson, John, 2008. "Large deviations of bootstrapped U -statistics," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1793-1806, September.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1793-1806
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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. Keener, Robert W. & Robinson, John & Weber, Neville C., 1998. "Tail probability approximations for U-statistics," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 59-65, January.
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    Cited by:

    1. 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.

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