A bounded N-tuplewise independent and identically distributed counterexample to the CLT |
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| Authors: | Alexander R Pruss |
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| Institution: | (1) Department of Philosophy, University of Pittsburgh, Pittsburgh, PA 15260, USA e-mail: pruss+@pitt.edu, US |
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| Abstract: | 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.
Received: 17 May 1996 / In revised form: 28 January 1998 |
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| Keywords: | Mathematics Subject Classification (1991): 60F0S |
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