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A strictly stationary, N-tuplewise independent counterexample to the Central Limit Theorem

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  • Bradley, Richard C.
  • Pruss, Alexander R.

Abstract

For an arbitrary integer N>=2, this paper gives the construction of a strictly stationary (and ergodic), N-tuplewise independent sequence of (nondegenerate) bounded random variables such that the Central Limit Theorem fails to hold. The sequence is in part an adaptation of a nonstationary example with similar properties constructed by one of the authors (ARP) in a paper published in 1998.

Suggested Citation

  • Bradley, Richard C. & Pruss, Alexander R., 2009. "A strictly stationary, N-tuplewise independent counterexample to the Central Limit Theorem," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3300-3318, October.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:10:p:3300-3318
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    Cited by:

    1. Tone, Cristina, 2016. "A central limit theorem for quadruple-wise independent arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 58-61.
    2. Beaulieu Guillaume Boglioni & de Micheaux Pierre Lafaye & Ouimet Frédéric, 2021. "Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin," Dependence Modeling, De Gruyter, vol. 9(1), pages 424-438, January.

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