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Entropy estimators and serial tests for ergodic chains

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1 Author(s)
Wegenkittl, S. ; Inst. fur Math., Salzburg Univ., Austria

Maurer (1992, A universal statistical test for random bit generators) discussed a statistic whose value is closely related to the per-bit-entropy of an ergodic stationary source. Here we derive an entropy estimate from a class of generalized serial tests and discuss its relationship to return-time-based entropy estimators and frequency-based goodness-of-fit tests. Our setup extends Kullback's I-divergence approach for independent stationary sequences to the class of ergodic Markov chains. The effects caused by the order of the source are examined theoretically and by an empirical study

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 6 )