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On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables

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  • Eghbal, N.
  • Amini, M.
  • Bozorgnia, A.

Abstract

Some Kolmogorov probability inequalities for quadratic forms and weighted quadratic forms of negative superadditive dependent (NSD) uniformly bounded random variables are provided. Using these inequalities, some complete convergence of randomized quadratic forms under some suitable conditions are evaluated. Moreover, various examples are presented in which the given conditions of our results are satisfied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1112-1120
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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. Eghbal, N. & Amini, M. & Bozorgnia, A., 2010. "Some maximal inequalities for quadratic forms of negative superadditive dependence random variables," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 587-591, April.
    5. Mavrikiou, Petroula M., 2008. "A Kolmogorov inequality for weighted U-statistics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3294-3297, December.
    6. 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.
    7. 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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    Cited by:

    1. Aiting Shen & Ying Zhang & Andrei Volodin, 2015. "Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 295-311, April.
    2. Xuejun Wang & Aiting Shen & Zhiyong Chen & Shuhe Hu, 2015. "Complete convergence for weighted sums of NSD random variables and its application in the EV regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 166-184, March.
    3. Boukhari, Fakhreddine, 2020. "The Marcinkiewics–Zygmund strong law of large numbers for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 161(C).

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