Quantization of probability distributions under norm-based distortion measures

DOI10.1524/stnd.22.4.261.64314zbMath1066.60026OpenAlexW4213404124MaRDI QIDQ3024663

Gilles Pagès, Sylvain Delattre, Siegfried Graf, Harald Luschgy

Publication date: 1 July 2005

Published in: Statistics & Decisions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1524/stnd.22.4.261.64314

zbMATH Keywords

weak convergenceempirical measurehigh-rate vector quantizationlocal distortionnorm-difference distortionpoint density measure

Mathematics Subject Classification ID

Fractals (28A80) Distribution theory (60E99) Source coding (94A29)

Related Items (18)

Optimal approximation and quantisation ⋮ Optimal Poisson quantisation ⋮ Constructive quantization: approximation by empirical measures ⋮ Asymptotics of the maximal radius of an \(L^{r}\)-optimal sequence of quantizers ⋮ Quantization dimensions of compactly supported probability measures via Rényi dimensions ⋮ The local quantization behavior of absolutely continuous probabilities ⋮ On the rate of convergence in Wasserstein distance of the empirical measure ⋮ Error bounds for high-resolution quantization with Rényi-\(\alpha\)-entropy constraints ⋮ The high resolution vector quantization problem with Orlicz norm distortion ⋮ Quantization of probability distributions under norm-based distortion measures. II: Self-similar distributions ⋮ Introduction to vector quantization and its applications for numerics ⋮ Distortion mismatch in the quantization of probability measures ⋮ Greedy vector quantization ⋮ Fractal functional quantization of mean-regular stochastic processes ⋮ Functional quantization for numerics with an application to option pricing ⋮ New weak error bounds and expansions for optimal quantization ⋮ New approach to greedy vector quantization ⋮ UniversalL^s-rate-optimality ofL^r-optimal quantizers by dilatation and contraction

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