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Strong law of large numbers for U-statistics of varying order

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  • Rempala, Grzegorz

Abstract

Let Unm be a U-statistic of order m based on n i.i.d. real random variables. Suppose that m=m(n) changes with n as n --> [infinity]. In this work we are concerned with establishing the strong consistency properties for Unm under linear norming. The results are obtained by generalizing the SLLN for arrays of rowwise independent random variables (Hu et al., 1989) to the case of rowwise martingale differences and applying standard martingale decompositions of Unm.

Suggested Citation

  • Rempala, Grzegorz, 1998. "Strong law of large numbers for U-statistics of varying order," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 263-270, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:3:p:263-270
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    References listed on IDEAS

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    1. Vitale, Richard A., 1992. "Covariances of symmetric statistics," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 14-26, April.
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