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Some maximal inequalities for quadratic forms of negative superadditive dependence random variables

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

Abstract

In this paper, we derive two maximal inequalities for quadratic forms of negative superadditive dependence random variables. Then, we obtain the strong law of large numbers and the rate of convergence under some suitable conditions on existence of moment. Noting that, the dependence structure that has been studied is an extension of negative association and sometimes more useful than it and can be used to get many important probability inequalities.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:587-591
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    References listed on IDEAS

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    1. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    2. Shanchao, Yang, 2006. "Moment inequalities for sums of products of independent random variables," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1994-2000, December.
    3. Bhattacharya, P.K., 2005. "A maximal inequality for nonnegative submartingales," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 11-12, April.
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    Cited by:

    1. 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.
    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. Xuejun Wang & Yi Wu & Shuhe Hu, 2018. "Strong and weak consistency of LS estimators in the EV regression model with negatively superadditive-dependent errors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 41-65, January.

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