Abstract
We extend some rate of convergence results of greedy quantization sequences already investigated in 2015. We show, for a more general class of distributions satisfying a certain control, that the quantization error of these sequences has an optimal rate of convergence and that the distortion mismatch property is satisfied. We will give some non-asymptotic Pierce type estimates. The recursive character of greedy vector quantization allows some improvements to the algorithm of computation of these sequences and the implementation of a recursive formula to quantization-based numerical integration. Furthermore, we establish further properties of sub-optimality of greedy quantization sequences.
Acknowledgements
The authors would like to express a sincere gratitude to, Dr. Rami El Haddad, the co-advisor of R. El Nmeir, for his help and advice during this work. Also, they would like to acknowledge the National Council for Scientific Research of Lebanon (CNRS-L) for granting a doctoral fellowship to Rancy El Nmeir, in a joint program with Agence Universitaire de la Francophonie of the Middle East and the research council of Saint-Joseph University of Beirut.
The third author benefited from the support of the “Chaire Risques Financiers”, Fondation du Risque.
Citation
Rancy El Nmeir. Harald Luschgy. Gilles Pagès. "New approach to greedy vector quantization." Bernoulli 28 (1) 424 - 452, February 2022. https://doi.org/10.3150/21-BEJ1350
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