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

TitleLocal distortion and µ-mass of the cells of one dimensional asymptotically optimal quantizers
Publication TypeJournal Article
Year of Publication2004
AuthorsSylvain Delattre, Jean-Claude Fort, and Gilles Pagès
JournalCommunications in Statistics. Theory and Methods
Volume33(5)
Start Page1087-1117
Date Published2004
Abstract

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.