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The convergence rates of the weighted bootstrap distributions for von Mises and -statistics

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  • Shuran Zhao
  • Xingzhong Xu
  • Xiaobo Ding

Abstract

It has been proved that the weighted bootstrap method for von Mises and U-statistics provides a feasible approximation to their sample distributions. In the paper, based on a variation of the Berry-Esseen theorem for U-statistics, we further develop such first-order convergence rate under weak conditions. Moreover, in view of maximum entropy, we provide a principle to choose the weights.

Suggested Citation

  • Shuran Zhao & Xingzhong Xu & Xiaobo Ding, 2008. "The convergence rates of the weighted bootstrap distributions for von Mises and -statistics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 645-660.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:645-660
    DOI: 10.1080/10485250802280259
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    1. Dehling, H. & Mikosch, T., 1994. "Random Quadratic Forms and the Bootstrap for U-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 392-413, November.
    2. Husková, Marie & Jansen, Paul, 1993. "Generalized bootstrat for studentized U-statistics: A rank statistic approach," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 225-233, February.
    3. Aerts, Marc & Janssen, Paul, 1995. "Weighted bootstrapping for U-quantiles," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 317-323, March.
    4. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
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