The local quantization behavior of absolutely continuous probabilities

• Autores: Siegfried Graf, Harald Luschgy, Gilles Pagès
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 4, 2012, págs. 1795-1828
• Idioma: inglés
• DOI: 10.1214/11-AOP663
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• Resumen

  • For a large class of absolutely continuous probabilities P it is shown that, for r>0, for n-optimal Lr(P)-codebooks αn, and any Voronoi partition Vn,a with respect to αn the local probabilities P(Vn,a) satisfy P(Va,n)≈n−1 while the local Lr-quantization errors satisfy ∫Vn,a∥x−a∥rdP(x)≈n−(1+r/d) as long as the partition sets Vn,a intersect a fixed compact set K in the interior of the support of P.