Please use this identifier to cite or link to this item: https://doi.org/10.1007/s11425-012-4527-3
Title: Self-normalized moderate deviations for independent random variables
Authors: Jing, B.Y.
Liang, H.Y.
Zhou, W. 
Keywords: increment
LIL
moderate deviation
self-normalized sum
t-statistic
Issue Date: 2012
Citation: Jing, B.Y., Liang, H.Y., Zhou, W. (2012). Self-normalized moderate deviations for independent random variables. Science China Mathematics 55 (11) : 2297-2315. ScholarBank@NUS Repository. https://doi.org/10.1007/s11425-012-4527-3
Abstract: Let X 1,X 2,... be a sequence of independent random variables (r. v. s) belonging to the domain of attraction of a normal or stable law. In this paper, we study moderate deviations for the self-normalized sum Σ i=1 nX i/V n,p where V n,p = (Σ i=1 n{pipe}X i{pipe} p) 1/p (p > 1). Applications to the self-normalized law of the iterated logarithm, Studentized increments of partial sums, t-statistic, and weighted sum of independent and identically distributed (i. i. d.) r. v. s are considered. © 2012 Science China Press and Springer-Verlag Berlin Heidelberg.
Source Title: Science China Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/105350
ISSN: 16747283
DOI: 10.1007/s11425-012-4527-3
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