Cramér-Type Moderate Deviation for Studentized Compound Poisson Sum

Bing-Yi Jing (), Qiying Wang () and Wang Zhou ()
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Bing-Yi Jing: Hong Kong University of Science and Technology
Qiying Wang: University of Sydney
Wang Zhou: National University of Singapore

Journal of Theoretical Probability, 2015, vol. 28, issue 4, 1556-1570

Abstract: Abstract Let $$N$$ N be a Poisson distributed random variable (r.v.) with parameter $$\lambda $$ λ . Let $$\{X, X_i, i \ge 1\}$$ { X , X i , i ≥ 1 } be a sequence of i.i.d. r.v’s that are independent of $$N$$ N . Set $$S_N=\sum _{j=1}^NX_j$$ S N = ∑ j = 1 N X j and $$V_N^2=\sum _{j=1}^NX_j^2$$ V N 2 = ∑ j = 1 N X j 2 . Assume that $$0

Keywords: Cramér large deviation; Self-normalized compound Poisson sum; Studentized compound Poisson sum; 62E20; 60G50 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-014-0542-3

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