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Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails

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  • Shen, Xinmei
  • Lin, Zhengyan

Abstract

Let {Xk,k>=1} be a sequence of negatively dependent random variables with common distribution F and mean 0. Suppose that is positive for all x and consistently varying as x-->[infinity]. Let {[theta]k,k>=1} be another sequence of random variables independent of {Xk,k>=1} satisfying P(a =1. The paper investigates large deviations for the randomly weighted sums.

Suggested Citation

  • Shen, Xinmei & Lin, Zhengyan, 2008. "Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3222-3229, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3222-3229
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    References listed on IDEAS

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    1. Ng, K.W. & Tang, Q.H. & Yang, H., 2002. "Maxima of Sums of Heavy-Tailed Random Variables," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 43-55, May.
    2. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.
    3. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    4. Hu, Tien-Chung & Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 155-164, January.
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    Cited by:

    1. Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 821-833, December.

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