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

https://hal.archives-ouvertes.fr/hal-00521185
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

local_quantization.pdf
Files produced by the author(s)

Identifiers

Citation

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 ; http://dx.doi.org/10.1214/11-AOP663. ⟨10.1214/11-AOP663⟩. ⟨hal-00521185⟩

Share

Metrics

Record views

620

Files downloads

515