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 ${ℝ}^{d}$ when $s>r$. In particular we show that under natural assumptions, the optimal rate is preserved as long as $s (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 : https://doi.org/10.1051/ps:2007044
Classification : 60G15,  60G35,  41A25
Mots clés : optimal quantization, Zador theorem
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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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