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.
|Pages (from-to)||229 - 241|
|Number of pages||13|
|Journal||Journal of Statistical Planning and Inference|
|Publication status||Published - 1992|