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Central limit theorem for dependent multidimensionally indexed random variables

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  • Christofides, Tasos C.
  • Mavrikiou, Petroula M.

Abstract

We consider dependent multidimensionally indexed random variables whose dependence is determined by the distance of their indices. This provides a generalization of the well-known notion of m-dependence. For the partial sum of a collection of such variables we prove a central limit theorem.

Suggested Citation

  • Christofides, Tasos C. & Mavrikiou, Petroula M., 2003. "Central limit theorem for dependent multidimensionally indexed random variables," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 67-78, May.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:1:p:67-78
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    References listed on IDEAS

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    1. Christofides, Tasos C. & Serfling, Robert, 1998. "U-statistics on a lattice of I.I.D. random variables," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 293-303, October.
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    Cited by:

    1. Harvey, Danielle J. & Weng, Qian & Beckett, Laurel A., 2010. "On an asymptotic distribution of dependent random variables on a 3-dimensional lattice," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1015-1021, June.
    2. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.

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