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A Note on Edgeworth Expansions for U-Statistics under Minimal Conditions

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Abstract

A one-term Edgeworth expansion for U-statistics with kernel h(x, y) was derived by Jing and Wang [3] under optimal moment conditions. In this note, we show that one of the optimal moment conditions E| h(X 1, X 2|5/3 < ∞ can be weakened to lim t→∞ t 5/3 P(|h(X 1, X 2)| > t) → 0.

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REFERENCES

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    B.-Y. Jing

  2. Department of Statistics and Applied Probability, National University of Singapore, 117546, Singapore

    W. Zhou

Authors
  1. B.-Y. Jing
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  2. W. Zhou
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Additional information

Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 453–440, July–September, 2005.

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Jing, BY., Zhou, W. A Note on Edgeworth Expansions for U-Statistics under Minimal Conditions. Lith Math J 45, 353–358 (2005). https://doi.org/10.1007/s10986-005-0036-1

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  • DOI: https://doi.org/10.1007/s10986-005-0036-1

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