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2011 Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails
Stefan Junglen
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Electron. Commun. Probab. 16: 283-295 (2011). DOI: 10.1214/ECP.v16-1629

Abstract

In this paper, we provide the sharp asymptotics for the quantization radius (maximal radius) for a sequence of optimal quantizers for random variables $X$ in $(\mathbb{R}^d,\|\,\cdot\,\|)$ with radial exponential tails. This result sharpens and generalizes the results developed for the quantization radius in [4] for $d > 1$, where the weak asymptotics is established for similar distributions in the Euclidean case. Furthermore, we introduce quantization balls, which provide a more general way to describe the asymptotic geometric structure of optimal codebooks, and extend the terminology of the quantization radius.

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Stefan Junglen. "Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails." Electron. Commun. Probab. 16 283 - 295, 2011. https://doi.org/10.1214/ECP.v16-1629

Information

Accepted: 6 June 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1239.60014
MathSciNet: MR2811180
Digital Object Identifier: 10.1214/ECP.v16-1629

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