@article{ECP1457,
author = {Elizabeth Meckes},
title = {Quantitative asymptotics of graphical projection pursuit},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {14},
year = {2009},
keywords = {Projection pursuit, concentration inequalities, Stein's method, Lipschitz distance},
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.},
pages = {no. 17, 176-185},
issn = {1083-589X},
doi = {10.1214/ECP.v14-1457},
url = {http://ecp.ejpecp.org/article/view/1457}}