Optimal quantizers for Radon random vectors in a Banach space
Probability
2016-08-16 v1
Abstract
For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e\_{n,r}(X,E) = inf{(E (\min\_{a \in \alpha} || X-a ||^r)^{1/r}}, where the infimum is taken over all subsets \alpha of E with card(\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.
Cite
@article{arxiv.math/0504236,
title = {Optimal quantizers for Radon random vectors in a Banach space},
author = {Siegried Graf and Harald Luschgy and Pagès Gilles},
journal= {arXiv preprint arXiv:math/0504236},
year = {2016}
}