Authors:
István Berkes A. Rényi Institute of Mathematics Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics P.O. Box 127, H-1364 Budapest Hungary Budapest P.O. Box 127, H-1364 Budapest Hungary Budapest

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Lajos Horváth Department of Mathematics University of Utah 155 South 1440 East Salt Lake City, UT 84112-0090 USA 155 South 1440 East Salt Lake City, UT 84112-0090 USA

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Piotr Kokoszka Department of Mathematics and Statistics Utah State University 3900 Old Main Hill Logan, UT 84322-3900 USA 3900 Old Main Hill Logan, UT 84322-3900 USA

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Qi-man Shao Department of Mathematics University of Oregon Eugene, OR 97403-1222\ USA Eugene, OR 97403-1222\ USA

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Summary  

We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary weekly dependent process. We also study the a.\ s.\ behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that, after appropriate normalization, the estimator converges a.s. in the long-range dependent case as well. In both cases, our conditions involve fourth order cumulants and assumptions on the rate of growth of the truncation parameter appearing in the definition of the Bartlett estimator.

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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