Rate of convergence in a theorem of Heyde

Let {X,Xn,n≥1} be a sequence of i.i.d. random variables with mean zero, and set Sn=∑k=1nXk, TX(t)=EX2I(|X|>t). Heyde (1975) proved precise asymptotics for ∑n=1∞P(|Sn|≥nϵ) as ϵ↘0. In this paper, we obtain a convergence rate in a theorem of Heyde (1975) under a second moment assumption only. Furthermore, under the additional assumption of TX(t)=O(t−δ) as t→∞ for some δ>0, we obtain a refined result.

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Year of publication:	2012
Authors:	Xie, Tingfan ; He, Jianjun
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 8, p. 1576-1582
Publisher:	Elsevier
Subject:	Theorem of Heyde \| Rate of approximation \| I.i.d random variable \| Precise asymptotics

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

Persistent link: https://www.econbiz.de/10011040101