@article{ECP1418,
author = {Joseph Yukich},
title = {Limit theorems for multi-dimensional random quantizers},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {13},
year = {2008},
keywords = {Quantization; laws of large numbers; central limit theorems; stabilization},
abstract = {We consider the $r$-th power quantization error arising in the optimal approximation of a $d$-dimensional probability measure $P$ by a discrete measure supported by the realization of $n$ i.i.d. random variables $X_1,...,X_n$. For all $d \geq 1$ and $r \in (0, \infty)$ we establish mean and variance asymptotics as well as central limit theorems for the $r$-th power quantization error. Limiting means and variances are expressed in terms of the densities of $P$ and $X_1$. Similar convergence results hold for the random point measures arising by placing at each $X_i, 1 \leq i \leq n,$ a mass equal to the local distortion.},
pages = {no. 48, 507-517},
issn = {1083-589X},
doi = {10.1214/ECP.v13-1418},
url = {http://ecp.ejpecp.org/article/view/1418}}