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Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly
2001 Vol.2 No.1 P.79-83
A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS
Abstract: Suppose {X,Xn;n≥1} is a sequence i.i.d.r.v. with EX=0 and EX2<∞. Shao (1995) proved a conjecture of Révész (1990): if P(X=±1)=1/2, then ... Furthermore he conjectured that ... In this paper we prove that if supb>0P(X=b)≥P(X=0) then this conjecture is true.
Key words: self-normalized,i.i.d.random variables,Chernoff function
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DOI:
10.1631/jzus.2001.0079
CLC number:
O211.4
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Received:
1999-10-18
Revision Accepted:
2000-04-18
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