Quantitative asymptotics of graphical projection pursuit

@article{Meckes2008QuantitativeAO,
  title={Quantitative asymptotics of graphical projection pursuit},
  author={Elizabeth S. Meckes},
  journal={arXiv: Probability},
  year={2008}
}
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 deterministic vectors $\{x_i\}_{i=1}^n$ in $\R^d$ with $n$ and $d$ fixed, let $\theta\in\s^{d-1}$ be a random point of the sphere and let $\mu_n^\theta$ denote the random measure which puts mass $\frac{1}{n}$ at each of the points… 
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