Distortion mismatch in the quantization of probability measures
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 127-153.

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 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 d and on the Wiener space.

DOI : https://doi.org/10.1051/ps:2007044
Classification : 60G15,  60G35,  41A25
Mots clés : optimal quantization, Zador theorem
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     author = {Graf, Siegfried and Luschgy, Harald and Pag\`es, Gilles},
     title = {Distortion mismatch in the quantization of probability measures},
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     pages = {127--153},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2007044/}
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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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