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

Xiaoyong Xiao and Hongwei Yin

Statistics & Probability Letters, 2012, vol. 82, issue 8, 1590-1596

Abstract: 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.

Keywords: Moment convergence; The law of iterated logarithm; I.i.d. random variables (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.04.019

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