Concentration bounds for entropy estimation of one-dimensional Gibbs measures
Dynamical Systems
2015-05-27 v2 Probability
Chaotic Dynamics
Abstract
We obtain bounds on fluctuations of two entropy estimators for a class of one-dimensional Gibbs measures on the full shift. They are the consequence of a general exponential inequality for Lipschitz functions of n variables. The first estimator is based on empirical frequencies of blocks scaling logarithmically with the sample length. The second one is based on the first appearance of blocks within typical samples.
Keywords
Cite
@article{arxiv.1102.1816,
title = {Concentration bounds for entropy estimation of one-dimensional Gibbs measures},
author = {J. -R. Chazottes and C. Maldonado},
journal= {arXiv preprint arXiv:1102.1816},
year = {2015}
}
Comments
12 pages, minor corrections made. To appear in Nonlinearity