THE LOCAL QUANTIZATION BEHAVIOR OF ABSOLUTELY CONTINUOUS PROBABILITIES

• 成果类型: Article
• 署名作者: Graf, Siegfried; Luschgy, Harald; Pages, Gilles
• 署名单位: University of Passau; Universitat Trier; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP663
• 发表日期: 2012
• 页码: 1795-1828
• 关键词: Asymptotics; quantizers; error

摘要

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,V-a with respect to alpha(n) the local probabilities P(V-n,V-a) satisfy P(V-a,V-n) approximate to n(-1) while the local L-r-quantization errors satisfy integral V-n,V-a parallel to x - a parallel to(r) d P (x) approximate to n(-(1+r/d)) as long as the partition sets V-n,V-a intersect a fixed compact set K in the interior of the support of P.