Precise asymptotics in the law of the iterated logarithm for R/S statistic

Title
Precise asymptotics in the law of the iterated logarithm for R/S statistic
Author(s)
황교신Tian-Xiao Pang[Tian-Xiao Pang]Zhengyan Lin[Zhengyan Lin]
Keywords
LARGE NUMBERS; RANGE
Issue Date
201403
Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
Citation
JOURNAL OF INEQUALITIES AND APPLICATIONS
Abstract
Let {X, X-n, n >= 1} be a sequence of i.i.d. random variables which is in the domain of attraction of the normal law with zero mean and possibly infinite variance, Q(n) = R(n)/S(n) be the rescaled range statistic, where R(n) = max(1 <= k <= n){Sigma(k)(j=1) (X-j - (X) over bar (n))} - min(1 <= k <= n){Sigma(k)(j=1) (X-j - (X) over bar (n))}, S-2(n) = Sigma(n)(j=1) (X-j - (X) over bar (n))(2/n) and (X) over bar (n) = Sigma(n)(j=1) X-j/n. Then two precise asymptotics related to probability convergence for Q(n) statistic are established under some mild conditions in this paper. Moreover, the precise asymptotics related to almost surely convergence for Q(n) statistic is also considered under some mild conditions.
URI
http://hdl.handle.net/YU.REPOSITORY/32795http://dx.doi.org/10.1186/1029-242X-2014-137
ISSN
1029-242X
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기초교육대학 > 교양학부 > Articles
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