Electronic Communications in Probability

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

David Mason and Joel Zinn

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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.

Article information

Source
Electron. Commun. Probab., Volume 10 (2005), paper no. 8, 70-81.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058073

Digital Object Identifier
doi:10.1214/ECP.v10-1135

Mathematical Reviews number (MathSciNet)
MR2133894

Zentralblatt MATH identifier
1112.60015

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Mason, David; Zinn, Joel. When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?. Electron. Commun. Probab. 10 (2005), paper no. 8, 70--81. doi:10.1214/ECP.v10-1135. https://projecteuclid.org/euclid.ecp/1465058073


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References

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