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When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?


 
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1. Title Title of document When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?
 
2. Creator Author's name, affiliation, country David M. Mason; University of Delaware, USA
 
2. Creator Author's name, affiliation, country Joel Zinn; Texas A&M University, USA
 
3. Subject Discipline(s)
 
3. Subject Keyword(s)
 
4. Description Abstract We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize the asymptotic distribution of relative sums and to provide a short proof of a 1973 conjecture of Logan, Mallows, Rice and Shepp on the asymptotic distribution of self--normalized sums in the case of symmetry.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2005-04-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1135
 
10. Identifier Digital Object Identifier 10.1214/ECP.v10-1135
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 10
 
12. Language English=en
 
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