An estimate of the remainder of a limit theorem

Jianjun He

Statistics & Probability Letters, 2012, vol. 82, issue 3, 478-487

Abstract: Let {X,Xn,n≥1} be a sequence of i.i.d. random variables with zero mean and finite variance. Set Sn=∑k=1nXk, EX2=σ2>0, λα(ϵ)=∑n=1∞P(|Sn|≥n1/2+αϵ), 0<α<1. In this paper, we discuss the rate of the approximation of σ1/αcα by ϵ1/αλα(ϵ) under suitable conditions, and extend the results of Klesov (1994), and He and Xie (in press), where cα=π−1/221/2αΓ(12+12α).

Keywords: The rate of approximation; I.i.d. random variable; Complete convergence (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.11.009

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