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

   
@article{ECP1135,
	author = {David Mason and Joel Zinn},
	title = {When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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.},
	pages = {no. 8, 70-81},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1135},    
        url = {http://ecp.ejpecp.org/article/view/1135}}