Skip to Main content Skip to Navigation
Journal articles

The local quantization behaviour of absolutely continuous probabilities

Abstract : For a large class of absolutely continuous probabilities P it is shown that, for r > 0, for n-optimal L^r(P)-codebooks \alpha_n, and any Voronoi partition V_{n,a} with respect to \alpha_n the local probabilities P(V_{n,a}) satisfy P(V_{a,n}) \approx n^{-1} while the local L^r-quantization errors satis\-fy $\int_{V_{n,a}} \|x-a\|^r dP(x) \approx n^{- (1+ \frac rd)}$ as long as the partition sets V_{n,a} intersect a fixed compact set K in the interior of the support of P.
Document type :
Journal articles
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download
Contributor : Gilles Pagès <>
Submitted on : Sunday, September 26, 2010 - 3:48:38 PM
Last modification on : Thursday, December 10, 2020 - 12:36:13 PM
Long-term archiving on: : Monday, December 27, 2010 - 2:35:02 AM


Files produced by the author(s)



Siegried Graf, Harald Luschgy, Gilles Pagès. The local quantization behaviour of absolutely continuous probabilities. Annals of Probability, Institute of Mathematical Statistics, 2012, 40 (4), 1795-1828 ; ⟨10.1214/11-AOP663⟩. ⟨hal-00521185⟩



Record views


Files downloads