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Asymptotic results for empirical measures of weighted sums of independent random variables

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Asymptotic results for empirical measures of weighted sums of independent random variables
2.	Creator	Author's name, affiliation, country	Bernard Bercu; Universite Bordeaux 1
2.	Creator	Author's name, affiliation, country	Wlodek Bryc; University of Cincinnati
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	We investigate the asymptotic behavior of weighted sums of independent standardized random variables with uniformly bounded third moments. The sequence of weights is given by a family of rectangular matrices with uniformly small entries and approximately orthogonal rows. We prove that the empirical CDF of the resulting partial sums converges to the normal CDF with probability one. This result implies almost sure convergence of empirical periodograms, almost sure convergence of spectral distribution of circulant and reverse circulant matrices, and almost sure convergence of the CDF generated from independent random variables by independent random orthogonal matrices. In the special case of trigonometric weights, the speed of the almost sure convergence is described by a normal approximation as well as a large deviation principle.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF grant DMS-0504198
7.	Date	(YYYY-MM-DD)	2007-05-24
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1273
10.	Identifier	Digital Object Identifier	10.1214/ECP.v12-1273
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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