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

   
@article{ECP1629,
	author = {Stefan Junglen},
	title = {Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {},
	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.},
	pages = {no. 27, 283-295},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1629},    
        url = {http://ecp.ejpecp.org/article/view/1629}}