Please use this identifier to cite or link to this item: https://doi.org/10.1214/aop/1065725185
Title: Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation
Authors: Horváth, L.
Shao, Q.-M. 
Keywords: Domain of attraction
Large deviation
Largest absolute observation
Law of the iterated logarithm
Self-normalized partial sums
Stable law
Issue Date: Jul-1996
Citation: Horváth, L., Shao, Q.-M. (1996-07). Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation. Annals of Probability 24 (3) : 1368-1387. ScholarBank@NUS Repository. https://doi.org/10.1214/aop/1065725185
Abstract: Let {Xn, 1 ≤ n ≤ ∞} be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index 0 < α < 2. The limit of x-1 n log P{Sn/ max |Xi|≥ xn} is found when xn → ∞ and xn/n → 0. The large deviation result is used to prove the law of the iterated logarithm for the self-normalized partial sums.
Source Title: Annals of Probability
URI: http://scholarbank.nus.edu.sg/handle/10635/103480
ISSN: 00911798
DOI: 10.1214/aop/1065725185
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