# Distortion mismatch in the quantization of probability measures

Siegfried Graf; Harald Luschgy; Gilles Pagès

ESAIM: Probability and Statistics (2008)

- Volume: 12, page 127-153
- ISSN: 1292-8100

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topGraf, Siegfried, Luschgy, Harald, and Pagès, Gilles. "Distortion mismatch in the quantization of probability measures." ESAIM: Probability and Statistics 12 (2008): 127-153. <http://eudml.org/doc/250412>.

@article{Graf2008,

abstract = {
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a
probability distribution P on $\mathbb\{R\}^d$ 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 $\mathbb\{R\}^d$ and on the Wiener space.
},

author = {Graf, Siegfried, Luschgy, Harald, Pagès, Gilles},

journal = {ESAIM: Probability and Statistics},

keywords = {Optimal quantization; Zador Theorem; Zador theorem},

language = {eng},

month = {1},

pages = {127-153},

publisher = {EDP Sciences},

title = {Distortion mismatch in the quantization of probability measures},

url = {http://eudml.org/doc/250412},

volume = {12},

year = {2008},

}

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

DA - 2008/1//

PB - EDP Sciences

VL - 12

SP - 127

EP - 153

AB -
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a
probability distribution P on $\mathbb{R}^d$ 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 $\mathbb{R}^d$ and on the Wiener space.

LA - eng

KW - Optimal quantization; Zador Theorem; Zador theorem

UR - http://eudml.org/doc/250412

ER -

## References

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