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

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Abstract

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.
Original language English 229 - 241 13 Journal of Statistical Planning and Inference 32 Published - 1992

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Random variables
Central limit theorem
M-sequence
Dependent
Term
Double Sequences
Score Function
Random variable
Theorem

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@article{498910c5bca44329b633e2dde6a8c13a,
title = "Central limit theorems for sequences with m(n)-dependent main part",
abstract = "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.",
author = "G. Nieuwenhuis",
year = "1992",
language = "English",
volume = "32",
pages = "229 -- 241",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",

}

In: Journal of Statistical Planning and Inference, Vol. 32, 1992, p. 229 - 241.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Central limit theorems for sequences with m(n)-dependent main part

AU - Nieuwenhuis, G.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

M3 - Article

VL - 32

SP - 229

EP - 241

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

ER -