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A Kolmogorov inequality for U-statistics based on Bernoulli kernels

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  • Christofides, Tasos C.

Abstract

A Kolmogorov inequality for the class of U-statistics based on kernels which are Bernoulli random variables is presented. This class of statistics contains the sample average of i.i.d. Bernoulli random variables as a special case. For this particular statistic, the bound obtained here is sharper than the one presented by Turner (1992).

Suggested Citation

  • Christofides, Tasos C., 1994. "A Kolmogorov inequality for U-statistics based on Bernoulli kernels," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 357-362, December.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:5:p:357-362
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    Cited by:

    1. Mavrikiou, Petroula M., 2007. "Kolmogorov inequalities for the partial sum of independent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1117-1122, June.
    2. Eghbal, N. & Amini, M. & Bozorgnia, A., 2011. "On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1112-1120, August.
    3. Mavrikiou, Petroula M., 2008. "A Kolmogorov inequality for weighted U-statistics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3294-3297, December.

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