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Central limit theorems for sequences with m(n)-dependent main part

By G. Nieuwenhuis


Let (Xi(n); n ϵ N, 1⩽i⩽h(n)) be a double sequence of random variables with h(n)→∞ as n→∞. Suppose that the sequence can be split into two parts: an m(n)-dependent sequence (Xi,m(n); n ϵ N, 1⩽i⩽h(n)) of main terms and a sequence (Xi,m(n); n ϵ N, 1⩽i⩽h(n)) of residual terms. Here (m(n)) may be unbounded in N. Adding some conditions, especially on the residual terms, we consider central limit theorems for (Xi(n)) based on a theorem for m(n)-dependent sequences. The results are of special interest when score functions are involved, for instance in rank-based procedures

Year: 1992
DOI identifier: 10.1016/0378-3758(92)90049-x
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Provided by: NARCIS
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