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April 2002 Rates of convergence for the empirical quantization error
Siegfried Graf, Harald Luschgy
Ann. Probab. 30(2): 874-897 (April 2002). DOI: 10.1214/aop/1023481010

Abstract

For $n, k \in \mathbb{N}$ and $r > 0$ let $e_{n,r}(P_k)^r = \inf 1/k \sum_{i=1}^k ||X_i - f(X_i)||^r$, where the infimum is taken over all measurable maps $f : \mathbb{R}^d \to \mathbb{R}^d$ with $|f(\mathbb{R}^d)| \leq n$ and $X_1, \dots, X_k$ are i.i.d. $\mathbb{R}^d$-valued random variables. We analyse the asymptotic a.s. behaviour of the $n$th empirical quantization error $e_{n,r}(P_k)$.

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Siegfried Graf. Harald Luschgy. "Rates of convergence for the empirical quantization error." Ann. Probab. 30 (2) 874 - 897, April 2002. https://doi.org/10.1214/aop/1023481010

Information

Published: April 2002
First available in Project Euclid: 7 June 2002

zbMATH: 1018.60032
MathSciNet: MR1905859
Digital Object Identifier: 10.1214/aop/1023481010

Subjects:
Primary: 60E15 , 60F15
Secondary: 62H30 , 94A29

Keywords: $L_r$-error , empirical measure , empirical process , empirical quantization error , multidimensional quantization

Rights: Copyright © 2002 Institute of Mathematical Statistics

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