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Sum of arbitrarily dependent random variables

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1.	Title	Title of document	Sum of arbitrarily dependent random variables
2.	Creator	Author's name, affiliation, country	Ruodu Wang; University of Waterloo; Canada
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	central limit theorems; laws of large numbers; almost sure convergence; arbitrary dependence; regular variation
3.	Subject	Subject classification	60F15; 60F05
4.	Description	Abstract	In many classic problems of asymptotic analysis, it appears that the scaled average of a sequence of $F$-distributed random variables converges to $G$-distributed limit in some sense of convergence. In this paper, we look at the classic convergence problems from a novel perspective: we aim to characterize all possible  limits of the sum of a sequence of random variables under different choices of dependence structure.We show that under general tail conditions on two given distributions $F$ and $G$,  there always exists a sequence of   $F$-distributed random variables  such that the scaled average of the sequence converges to a $G$-distributed limit almost surely. We construct such a sequence of random variables via a structure of conditional independence. The results in this paper suggest that with the common marginal distribution fixed and dependence structure unspecified, the distribution of the sum of a sequence of random variables can be asymptotically of  any shape.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSERC
7.	Date	(YYYY-MM-DD)	2014-09-16
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/3373
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3373
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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