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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 |
Appears in Collections: | Staff Publications |
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