Universal L-rate-optimality of L-optimal quantizers by dilatation and contraction

Abstract

Let r, s > 0. For a given probability measure P on R, let (αn)n≥1 be a sequence of (asymptotically)L(P )optimal quantizers. For all μ ∈ R and for every θ > 0, one defines the sequence (α n )n≥1 by : ∀n ≥ 1, α n = μ+ θ(αn −μ) = {μ+ θ(a−μ), a ∈ αn}. In this paper, we are interested in the asymptotics of the L-quantization error induced by the sequence (α n )n≥1. We show that for a wide family of distributions, the sequence (α n )n≥1 is L -rate-optimal. For the Gaussian and the exponential distributions, one shows how to choose the parameter θ such that (α n )n≥1 satisfies the empirical measure theorem and probably be asymptotically L -optimal.

2 Figures and Tables

Cite this paper

@inproceedings{Sagna2008UniversalLO, title={Universal L-rate-optimality of L-optimal quantizers by dilatation and contraction}, author={Abass Sagna}, year={2008} }