Optimal quantizers for Radon random vectors in a Banach space

  • Authors:

  • Siegfried Graf;Harald Luschgy;Gilles Pagès

  • Affiliations:

  • Universität Passau, Fakultät für Mathematik und Informatik, D-94030 Passau, Germany;Universität Trier, FB IV-Mathematik, D-54286 Trier, Germany;Laboratoire de Probabilités et Modèles aléatoires, UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2007

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Abstract

For n@?N,r@?(0,~) and a Radon random vector X with values in a Banach space E let e"n","r(X,E)=inf(Emin"a"@?"@a@?X-a@?^r)^1^/^r, where the infimum is taken over all subsets @a of E with card(@a)=