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Optimal quantizers for Radon random vectors in a Banach space

Abstract : For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e_{n,r}(X,E) = inf{(E (\min_{a \in \alpha} || X-a ||^r )^{1/r}}, where the infimum is taken over all subsets \alpha of E with card(\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.
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Submitted on : Tuesday, April 12, 2005 - 10:10:13 AM
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Siegried Graf, Harald Luschgy, Gilles Pagès. Optimal quantizers for Radon random vectors in a Banach space. Journal of Approximation Theory, Elsevier, 2007, 144 (1), 27-53 ; http://dx.doi.org/10.1016/j.jat.2006.04.006. ⟨10.1016/j.jat.2006.04.006⟩. ⟨hal-00004668⟩

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