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The almost sure invariance principles of degenerate U-statistics of degree two for stationary random variables

Author

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  • Kanagawa, S.
  • Yoshihara, K.

Abstract

The almost sure invariance principle for some degenerate U-statistics of degree two is considered for strictly stationary random variables satisfying mixing conditions. The error term obtained is O(t1 - [gamma]) which yields Donsker's and Strassen's invariance principles for the U-statistics. The approach used here is based upon Hoeffding's expansion of kernel functions and the almost sure invariance principles for partial sums of Banach space valued mixing random variables.

Suggested Citation

  • Kanagawa, S. & Yoshihara, K., 1994. "The almost sure invariance principles of degenerate U-statistics of degree two for stationary random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 347-356, February.
    • Handle: RePEc:eee:spapps:v:49:y:1994:i:2:p:347-356
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    Cited by:

    1. Shuya Kanagawa, 2022. "Asymptotic Expansions for Symmetric Statistics with Degenerate Kernels," Mathematics, MDPI, vol. 10(21), pages 1-10, November.

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