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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Veröffentlicht in:	Journal of the Korean Statistical Society 2013, 42(2), , pp.177-189
Hauptverfasser:	Pang, Tian-Xiao, Lin, Zheng-Yan, Hwang, Kyo-Shin
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Zusammenfassung:	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.
ISSN:	1226-3192 2005-2863
DOI:	10.1016/j.jkss.2012.07.003