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Quantitative asymptotics of graphical projection pursuit

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Quantitative asymptotics of graphical projection pursuit
2.	Creator	Author's name, affiliation, country	Elizabeth S Meckes; Case Western Reserve University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Projection pursuit, concentration inequalities, Stein's method, Lipschitz distance
3.	Subject	Subject classification	60E15;62E20
4.	Description	Abstract	There is a result of Diaconis and Freedman which says that, in a limiting sense, for large collections of high-dimensional data most one-dimensional projections of the data are approximately Gaussian. This paper gives quantitative versions of that result. For a set of $n$ deterministic vectors $\{x_i\}$ in $R^d$ with $n$ and $d$ fixed, let $\theta$ be a random point of the sphere and let $\mu_\theta$ denote the random measure which puts equal mass at the projections of each of the $x_i$ onto the direction $\theta$. For a fixed bounded Lipschitz test function $f$, an explicit bound is derived for the probability that the integrals of $f$ with respect to $\mu_\theta$ and with respect to a suitable Gaussian distribution differ by more than $\epsilon$. A bound is also given for the probability that the bounded-Lipschitz distance between these two measures differs by more than $\epsilon$, which yields a lower bound on the waiting time to finding a non-Gaussian projection of the $x_i$, if directions are tried independently and uniformly.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	American Institute of Mathematics
7.	Date	(YYYY-MM-DD)	2009-05-03
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/1457
10.	Identifier	Digital Object Identifier	10.1214/ECP.v14-1457
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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