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Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails


 
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1. Title Title of document Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails
 
2. Creator Author's name, affiliation, country Stefan Junglen; University of Trier
 
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4. Description 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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7. Date (YYYY-MM-DD) 2011-06-06
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1629
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1629
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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