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Probability inequalities with exponential bounds for U-statistics

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  • Christofides, Tasos C.

Abstract

I present some probability inequalities with exponential bounds for U-statistics. In particular, I develop a probability inequality for U-statistics based on kernels which are Bernoulli random variables. In the special case of the simple average of i.i.d. Bernoulli random variables, the result provides a bound which is sharper than the results of Kambo and Kotz (1966) and Young, Turner and Seaman (1988).

Suggested Citation

  • Christofides, Tasos C., 1991. "Probability inequalities with exponential bounds for U-statistics," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 257-261, September.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:3:p:257-261
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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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