Open Access
2005 When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?
David Mason, Joel Zinn
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Electron. Commun. Probab. 10: 70-81 (2005). DOI: 10.1214/ECP.v10-1135


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.


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David Mason. Joel Zinn. "When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?." Electron. Commun. Probab. 10 70 - 81, 2005.


Accepted: 16 April 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1112.60015
MathSciNet: MR2133894
Digital Object Identifier: 10.1214/ECP.v10-1135

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