Precise asymptotics in the law of the logarithm for the rescaled range statistic

For a sequence of i.i.d. zero mean random variables belonging to the domain of attraction of the normal law, two results concerning the rescaled range statistic are investigated in this paper. More specifically, we obtain precise asymptotics in the law of the logarithm related to complete convergenc...

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Bibliographic Details
Published inJournal of the Korean Statistical Society Vol. 42; no. 2; pp. 177 - 189
Main Authors Pang, Tian-Xiao, Lin, Zheng-Yan, Hwang, Kyo-Shin
Format Journal Article
LanguageEnglish
Published Singapore Elsevier B.V 01.06.2013
Springer Singapore
한국통계학회
Subjects
A.s. convergence
Applied Statistics
Bayesian Inference
Complete convergence
Domain of attraction of the normal law
Law of the logarithm
Precise asymptotics
Rescaled range statistic
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
통계학
secondary
Precise asymptotics
Law of the logarithm
Complete convergence
A.s. convergence
Rescaled range statistic
Domain of attraction of the normal law
primary
primary 60F15
secondary 60G50
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Summary:For a sequence of i.i.d. zero mean random variables belonging to the domain of attraction of the normal law, two results concerning the rescaled range statistic are investigated in this paper. More specifically, we obtain precise asymptotics in the law of the logarithm related to complete convergence and a.s. convergence under some mild conditions.
Bibliography:G704-000337.2013.42.2.006
ISSN:1226-3192
2005-2863
DOI:10.1016/j.jkss.2012.07.003