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Negative association and negative dependence for random upper semicontinuous functions, with applications

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  • Thuan, Nguyen Tran
  • Quang, Nguyen Van

Abstract

The aim of this paper is to construct the notions of negative association and negative dependence for random upper semicontinuous functions. Besides giving some properties for these notions, we obtain inequalities which form maximal inequality and Hájek–Rényi’s type inequality. In addition, some laws of large numbers are established under various settings and they are extensions for corresponding ones in the literature.

Suggested Citation

  • Thuan, Nguyen Tran & Quang, Nguyen Van, 2016. "Negative association and negative dependence for random upper semicontinuous functions, with applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 44-57.
    • Handle: RePEc:eee:jmvana:v:145:y:2016:i:c:p:44-57
    DOI: 10.1016/j.jmva.2015.12.002
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    References listed on IDEAS

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    1. Daffer, Peter Z., 1991. "Convergence of weighted sums of random functions in D[0, 1]," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 319-332, August.
    2. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    3. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
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