We elucidate the asymptotics of the -quantization error induced by a sequence of -optimal -quantizers of a probability distribution on when . In particular we show that under natural assumptions, the optimal rate is preserved as long as (and for every in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
Mots-clés : optimal quantization, Zador theorem
@article{PS_2008__12__127_0,
author = {Graf, Siegfried and Luschgy, Harald and Pag\`es, Gilles},
title = {Distortion mismatch in the quantization of probability measures},
journal = {ESAIM: Probability and Statistics},
pages = {127--153},
publisher = {EDP-Sciences},
volume = {12},
year = {2008},
doi = {10.1051/ps:2007044},
mrnumber = {2374635},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps:2007044/}
}
TY - JOUR AU - Graf, Siegfried AU - Luschgy, Harald AU - Pagès, Gilles TI - Distortion mismatch in the quantization of probability measures JO - ESAIM: Probability and Statistics PY - 2008 SP - 127 EP - 153 VL - 12 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2007044/ DO - 10.1051/ps:2007044 LA - en ID - PS_2008__12__127_0 ER -
%0 Journal Article %A Graf, Siegfried %A Luschgy, Harald %A Pagès, Gilles %T Distortion mismatch in the quantization of probability measures %J ESAIM: Probability and Statistics %D 2008 %P 127-153 %V 12 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2007044/ %R 10.1051/ps:2007044 %G en %F PS_2008__12__127_0
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles. Distortion mismatch in the quantization of probability measures. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 127-153. doi : 10.1051/ps:2007044. http://www.numdam.org/articles/10.1051/ps:2007044/
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