Cramér’s type results for some bootstrapped U-statistics

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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.

Keywords

U-statistics Wild Bootstrap Large deviations 

Mathematics Subject Classification

60F10 60G50 62E20 

Notes

Acknowledgements

The authors are grateful to the Editor, an Associate editor, and the referees for thorough proofreading and numerous comments which led to a considerable improvement of the presentation of this paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Appliquées de CompiègneUniversité de Technologie de CompiègneCompiègne cedexFrance

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