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On weak approximations of U-statistics

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  • Nasari, Masoud M.

Abstract

This paper investigates weak convergence of U-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U-statistic exists is relaxed to having moments only (modulo a logarithmic term). Furthermore, the conditional expectation of the kernel is only assumed to be in the domain of attraction of the normal law (instead of the classical two-moment condition).

Suggested Citation

  • Nasari, Masoud M., 2009. "On weak approximations of U-statistics," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1528-1535, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:13:p:1528-1535
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    References listed on IDEAS

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    1. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Cited by:

    1. Chen, Willa W. & Deo, Rohit S., 2018. "Subsampling based inference for U statistics under thick tails using self-normalization," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 95-103.

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