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Tail probability approximations for U-statistics

Author

Listed:
  • Keener, Robert W.
  • Robinson, John
  • Weber, Neville C.

Abstract

Let Un be a second-degree, nondegenerate, zero mean U-statistic with a bounded kernel, scaled so that Un/[radical sign]n => N(0, [sigma]2). Large deviation approximations are developed for tail probabilities P(Un > x[radical sign]n) using a new explicit tilting procedure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:1:p:59-65
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Borovskikh, Yuri V. & Robinson, John, 2008. "Large deviations of bootstrapped U -statistics," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1793-1806, September.

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