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On construction of confidence intervals for a mean of dependent data

Jan Ćwik; Jan Mielniczuk

Discussiones Mathematicae Probability and Statistics (2001)

  • Volume: 21, Issue: 2, page 121-147
  • ISSN: 1509-9423

Abstract

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In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by Wu (2001) seems to perform most stably.

How to cite

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Jan Ćwik, and Jan Mielniczuk. "On construction of confidence intervals for a mean of dependent data." Discussiones Mathematicae Probability and Statistics 21.2 (2001): 121-147. <http://eudml.org/doc/287731>.

@article{JanĆwik2001,
abstract = {In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by Wu (2001) seems to perform most stably.},
author = {Jan Ćwik, Jan Mielniczuk},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {confidence intervals; short-range dependence; reuse block methods; normal approximation; iterated random function sequence; iterated random function sequences},
language = {eng},
number = {2},
pages = {121-147},
title = {On construction of confidence intervals for a mean of dependent data},
url = {http://eudml.org/doc/287731},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Jan Ćwik
AU - Jan Mielniczuk
TI - On construction of confidence intervals for a mean of dependent data
JO - Discussiones Mathematicae Probability and Statistics
PY - 2001
VL - 21
IS - 2
SP - 121
EP - 147
AB - In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by Wu (2001) seems to perform most stably.
LA - eng
KW - confidence intervals; short-range dependence; reuse block methods; normal approximation; iterated random function sequence; iterated random function sequences
UR - http://eudml.org/doc/287731
ER -

References

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  10. [10] H.C. Ho and T. Hsing, Limit theorems for functionals of moving averages, Ann. Probab. 25 (1997), 1636-1669. Zbl0903.60018
  11. [11] H. Künsch, The jacknife and the bootstrap for general stationary observations, Ann. Statist. 17 (1989), 1217-1241. Zbl0684.62035
  12. [12] Politis and Romano, Large sample confidence regions based on subsamples under minimal asuumptions, Ann. Statist. 22 (1994), 2031-2050. Zbl0828.62044
  13. [13] M. Rosenblatt, Stationary Sequences and Random Fields, Birkhäuser, Boston 1985. Zbl0597.62095
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  16. [16] W.B. Wu, Studies in time series and random dynamics, Ph. D. thesis, University of Michigan 2001. 

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