Summary.
A sequence of random variables X 1,X 2,X 3,… is said to be N-tuplewise independent if X i 1,X i 2,…,X i N are independent whenever (i 1,i 2,…,i N ) is an N-tuple of distinct positive integers. For any fixed N∈ℤ+, we construct a sequence of bounded identically distributed N-tuplewise independent random variables which fail to satisfy the central limit theorem.
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Received: 17 May 1996 / In revised form: 28 January 1998
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Pruss, A. A bounded N-tuplewise independent and identically distributed counterexample to the CLT. Probab Theory Relat Fields 111, 323–332 (1998). https://doi.org/10.1007/s004400050170
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DOI: https://doi.org/10.1007/s004400050170