Concentration bounds for entropy estimation of one-dimensional Gibbs measures

Details Concentration bounds for entropy estimation of one-dimensional Gibbs measures Concentration bounds for entropy estimation of one-dimensional Gibbs measures

2011-02-09

arxiv.org/abs/1102.1816v2

Mathematics

Dynamical Systems

12 pages, minor corrections made. To appear in Nonlinearity

Scientific paper

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.

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