Concentration bounds for entropy estimation of one-dimensional Gibbs measures
arXiv:1102.1816 · doi:10.1088/0951-7715/24/8/011
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.
12 pages, minor corrections made. To appear in Nonlinearity