A supplement to precise asymptotics in the law of the iterated logarithm |
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| Authors: | Deli Li Bao-Em Nguyen |
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| Institution: | a Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, Canada P7B 5E1
b Department of Statistics, University of Florida, Gainesville, FL 32611, USA |
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| Abstract: | Let  be a sequence of real-valued i.i.d. random variables with E(X)=0 and E(X2)=1, and set  , n?1. This paper studies the precise asymptotics in the law of the iterated logarithm. For example, using a result on convergence rates for probabilities of moderate deviations for  obtained by Li et al. Internat. J. Math. Math. Sci. 15 (1992) 481-497], we prove that, for every b∈(−1/2,1], |
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| Keywords: | Precise asymptotics Law of the iterated logarithm Convergence rates of moderate deviations Partial sums of i i d random variables |
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