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A Kolmogorov inequality for weighted U-statistics

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  • Mavrikiou, Petroula M.

Abstract

In this paper a Kolmogorov probability inequality for weighted U-statistics based on Bernoulli kernels is presented. This inequality which extends the results of [Turner, D.W., Young, D.M., Seaman, J.W., 1995. A Kolmogorov inequality for the sum of independent Bernoulli random variables with unequal means. Statist. Probab. Lett. 23, 243-245] is a Hoeffding type exponential inequality without any assumptions or restrictions.

Suggested Citation

  • Mavrikiou, Petroula M., 2008. "A Kolmogorov inequality for weighted U-statistics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3294-3297, December.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3294-3297
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    References listed on IDEAS

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    1. Christofides, Tasos C., 1991. "Probability inequalities with exponential bounds for U-statistics," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 257-261, September.
    2. 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.
    3. Turner, Danny W. & Young, Dean M. & Seaman, John W., 1995. "A Kolmogorov inequality for the sum of independent Bernoulli random variables with unequal means," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 243-245, May.
    4. 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.
    5. Young, Dean M. & Seaman, John W. & Marco, Virgil R., 1987. "A note on a Kolmogorov inequality," Statistics & Probability Letters, Elsevier, vol. 5(3), pages 217-218, April.
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    1. 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.

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