Local distortion and μ-mass of the cells of one dimensional asymptotically optimal quantizers

被引：7

作者：

Delattre, S

Fort, JC

Pagés, G

机构：

[1] Univ Toulouse 3, Lab Stat & Probabil, UMR C5583, F-31062 Toulouse 4, France

[2] Univ Paris 07, Dept Math, Lab Probabil & Modeles Aleatoires, Paris, France

[3] Univ Paris 01, SAMOS, F-75231 Paris 05, France

[4] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2004年 / 33卷 / 05期

关键词：

vector quantization; empirical measured; weak convergence; local distortion;

D O I：

10.1081/STA-120029827

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider one dimensional probability distributions mu having a continuous and positive probability density function. We find the asymptotic of the size and the mass of the Voronoi cells and we prove that the local distortion associated with stationary or optimal quantizers is asymptotically uniform. Numerical simulations and computations illustrate the theoretical results and lead to the design of some good-fit test for the stationary equilibria.

引用

页码：1087 / 1117

页数：31

共 22 条

[11]

Graf S., 2000, LECT NOTES MATH, V1730

[12] EXPONENTIAL RATE OF CONVERGENCE FOR LLOYDS METHOD-I [J].