Distortion mismatch in the quantization of probability measures

Siegried Graf (1) , Harald Luschgy (2) , Gilles Pagès (3)

1 UNIVERSITÄT PASSAU - Fakultät für Mathematik und Informatik
2 FB IV-Mathematik
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We elucidate the asymptotics of the L^s-quantization error induced by a sequence of L^r-optimal n-quantizers of a probability distribution P on R^d when s>r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s

Mots clés: Zador Theorem; numerical integration; Optimal quantization

Domaines: Probabilités [math.PR]

Siegried Graf, Harald Luschgy, Gilles Pagès. Distortion mismatch in the quantization of probability measures. ESAIM: Probability and Statistics, 2008, 12, 127-153 ; http://dx.doi.org/10.1051/ps:2007044. ⟨10.1051/ps:2007044⟩. ⟨hal-00019228⟩