An estimate of the remainder of a limit theorem

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).

MoreLess

Year of publication:	2012
Authors:	He, Jianjun
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 3, p. 478-487
Publisher:	Elsevier
Subject:	The rate of approximation \| I.i.d. random variable \| Complete convergence

Online Resource

Check full text access |

More access options

Check Google Scholar

In libraries world-wide (WorldCat)

In German libraries (KVK)

subito order

I need help

More details

Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011039848