Geodesic
Distortion mismatch in the quantization of probability measures
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 127-153 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

We elucidate the asymptotics of the L s -quantization error induced by a sequence of L r -optimal n-quantizers of a probability distribution P on ℝ d when s>r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s<r+d (and for every s 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 ℝ d and on the Wiener space.

DOI : 10.1051/ps:2007044
Classification : 60G15, 60G35, 41A25
Keywords: 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},
     year = {2008},
     publisher = {EDP-Sciences},
     volume = {12},
     doi = {10.1051/ps:2007044},
     mrnumber = {2374635},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :