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Quantization balls and asymptotics of quantization radii for probability distributions with radial exponential tails. (English) Zbl 1239.60014
Summary: 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 [G. Pagès and A. Sagna, Bernoulli 18, No. 1, 360–389 (2012; Zbl 1245.60052)] for \(d\geq 2\), 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.

MSC:
60E99 Distribution theory
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