Asymptotic analysis of the statistical estimators of Shannon entropy of binary s-tuples - Palukha, Uladzimir Yu.; Kharin, Yuriy S. (Journal of the Belarusian State University. Mathematics and Informatics, 2025)
The asymptotic probability distribution of the statistical estimate of Shannon entropy of s-tuples H(s) and the asymptotic joint probability distribution of the statistical estimates of Shannon entropy of s- and (s+1)-tuples H(s), H(s+1) for a uniformly distributed random binary sequence with increasing length are found. It is proved that as the value of s increase, the correlation coefficient of the statistical estimates of Shannon entropy of s- and (s+1)-tuples H(s), H(s+1) tends to zero. The theoretical results are illustrated by computer experiments.