### Abstract

Original language | English |
---|---|

Pages (from-to) | 229 - 241 |

Number of pages | 13 |

Journal | Journal of Statistical Planning and Inference |

Volume | 32 |

Publication status | Published - 1992 |

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*Journal of Statistical Planning and Inference*, vol. 32, pp. 229 - 241.

**Central limit theorems for sequences with m(n)-dependent main part.** / Nieuwenhuis, G.

Research output: Contribution to journal › Article › Scientific › peer-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 -