On the Self-Normalized Cramér-type Large Deviation

John Robinson () and Qiying Wang ()
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John Robinson: The University of Sydney
Qiying Wang: The University of Sydney

Journal of Theoretical Probability, 2005, vol. 18, issue 4, 891-909

Abstract: For the self-normalized sum, $$S_n/V_n$$ , it is shown that $$P(S_n/V_n\ge x)/(1-\Phi(x))$$ converges to 1, uniformly in a region, under the optimal assumption that the sampled distribution is in the domain of attraction of the normal law. Bounds for this convergence are given and their applications to exponential non-uniform Berry–Esseen bound are also discussed.

Keywords: Cramér large deviation; moderate deviation; non-uniform Berry–Esseen bound; domain of attraction of the normal law; self-normalized sum (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-005-7531-5

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