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 n i=1 X i /V n,p where V n,p = (Σ n i=1 |X i |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.
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Jing, B., Liang, H. & Zhou, W. Self-normalized moderate deviations for independent random variables. Sci. China Math. 55, 2297–2315 (2012). https://doi.org/10.1007/s11425-012-4527-3
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DOI: https://doi.org/10.1007/s11425-012-4527-3