@article {delattre,
title = {Quantization of probability distributions under norm-based distortion measures},
year = {2004},
note = {60{E}99, 94{A}29, 28{A}80},
abstract = {For a probability measure $P$ on $\mathbb{R}^d$ and $n \in \mathbb{N}$ consider $e_n = \inf \int \min_{a \in \alpha} V(\| x-a \| )dP(x)$ where the infimum is taken over all subsets $\alpha$ of $\{R}^d$ with $\mbox{card} (\alpha) \leq n$ and ${V}$ is a nondecreasing function. Under certain conditions on $V$, we derive the precise $n$-asymptotics of $e_n$ for nonsingular and for (singular) self-similar distributions $P$ and we find the asymptotic performance of optimal quantizers using weighted empirical measures.},
keywords = {empirical measure, High-rate vector quantization, local distortion, norm-difference distortion, Point density measure, weak convergence},
author = {Sylvain Delattre and Siegfried Graf and Harald Luschgy and Gilles Pag{\`e}s}
}