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2008 Limit theorems for multi-dimensional random quantizers
Joseph Yukich
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Electron. Commun. Probab. 13: 507-517 (2008). DOI: 10.1214/ECP.v13-1418


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 $ 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.


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Joseph Yukich. "Limit theorems for multi-dimensional random quantizers." Electron. Commun. Probab. 13 507 - 517, 2008.


Accepted: 13 October 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60054
MathSciNet: MR2447837
Digital Object Identifier: 10.1214/ECP.v13-1418

Primary: 60F05
Secondary: 60D05

Keywords: central limit theorems , laws of large numbers , quantization , stabilization

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