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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 8 open journal systems 


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

David M. Mason, University of Delaware, USA
Joel Zinn, Texas A&M University, USA


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.


Full text: PDF

Pages: 70-81

Published on: April 16, 2005
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Electronic Communications in Probability. ISSN: 1083-589X