@article {52,
title = {Quantization for probability measures in the Prokhorov metric},
journal = {Theory Probab. Appl.},
volume = {53},
year = {2009},
pages = {216-241},
abstract = {For a probability distribution $P$ on $\mathbb{R}^d$ and $n\in N$ consider $e_n=inf \pi(P,Q)$, where $\pi$ denotes the Prokhorov metric and the infimum is taken over all discrete probabilities $Q$ with $|\textrm{supp}(Q)|\leq n$. We study solutions $Q$ of this minimization problem, stability properties, and consistency of empirical estimators. For some classes of distributions we determine the exact rate of convergence to zero of the $n$th quantization error en as $n\to \infty$. },
keywords = {asymptotic quantization error, empirical measures, entropy, Ky Fan metric, multidimensional quantization, optimal quantizers, Prokhorov metric, quantization dimension},
author = {Harald Luschgy and Siegfried Graf}
}