Discussiones Mathematicae Probability and Statistics 21(2) (2001) 121-147

ON CONSTRUCTION OF CONFIDENCE INTERVALS FOR A MEAN OF DEPENDENT DATA

 Jan Ćwik

Institute of Computer Science, Polish Academy of Sciences
Ordona 21, 01-237 Warsaw, Poland
e-mail: jc@ipipan.waw.pl

Jan Mielniczuk

Institute of Computer Science, Polish Academy of Sciences
Ordona 21, 01-237 Warsaw, Poland
Polish-Japanese Institute of Computer Technologies
Koszykowa 86, 02-008 Warszaw, Poland
e-mail:
miel@ipipan.waw.pl

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.

Keywords:  confidence intervals;  short-range dependence;  reuse block methods;  normal approximation;  iterated random function sequence.

2000 Mathematics Subject Classification: Primary 62G15; Secondary 62G07.

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Received 9 January 2001