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An exponential inequality for associated variables

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  • Oliveira, Paulo Eduardo

Abstract

We prove an exponential inequality for positively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. The proof uses a truncation technique together with a block decomposition of the sums to allow an approximation to independence. We show that for geometrically decreasing covariances our conditions are fulfilled, identifying a convergence rate for the strong law of large numbers.

Suggested Citation

  • Oliveira, Paulo Eduardo, 2005. "An exponential inequality for associated variables," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 189-197, June.
  • Handle: RePEc:eee:stapro:v:73:y:2005:i:2:p:189-197
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    References listed on IDEAS

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    1. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
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    Cited by:

    1. Sung, Soo Hak, 2007. "A note on the exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1730-1736, December.
    2. Yang, Shanchao & Su, Chun & Yu, Keming, 2008. "A general method to the strong law of large numbers and its applications," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 794-803, April.
    3. Guodong Xing & Shanchao Yang, 2010. "Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 23(1), pages 169-192, March.

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    Keywords

    Association Exponential inequality;

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