Almost sure convergence of the Bartlett estimator

被引：0
|
作者：
Berkes I. [1 ,2 ]
Horváth L. [3 ]
Kokoszka P. [4 ]
Shao Q.-M. [5 ,6 ]
机构：
[1] Department of Statistics, Graz University of Technology, A-8010 Graz
[2] A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest
[3] Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090
[4] Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900
[5] Department of Mathematics, University of Oregon, Eugene
[6] Department of Statistics and Applied Probability, National University of Singapore
来源：
Periodica Mathematica Hungarica | 2005年 / 51卷 / 1期
关键词：
Cumulants; Increments of partial sums; Long-range dependence; Variance of the mean; Weak dependence;
D O I：
10.1007/s10998-005-0017-5
中图分类号：
学科分类号：
摘要：
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. © Akadémiai Kiadó.
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页码：11 / 25
页数：14
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