Concentration bounds for entropy estimation of one-dimensional Gibbs measures

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.