Precise asymptotics in the law of iterated logarithm for the first moment convergence of i.i.d. random variables

Let {X,Xn,n≥1} be a sequence of i.i.d. random variables and set Sn=∑i=1nXi. N is the standard normal random variable, then for d>0 and β>0, we show that limε↘0ε2β/d∑n=3∞(loglogn)β−1n3/2lognE{|Sn|−εσn(loglogn)d/2}+=dσE|N|2β/d+1β(2β+d) holds if and only if EX=0,EX2=σ2.

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Year of publication:	2012
Authors:	Xiao, Xiaoyong ; Yin, Hongwei
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 8, p. 1590-1596
Publisher:	Elsevier
Subject:	Moment convergence \| The law of iterated logarithm \| I.i.d. random variables

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

Persistent link: https://ebvufind01.dmz1.zbw.eu/10011040046