Asymptotic analysis of the statistical estimators of Shannon entropy of binary s-tuples
Keywords:
энтропия Шеннона, двоичная последовательность, статистическая оценка, ковариация, коэффициент корреляцииAbstract
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.
References
- Palukha UYu, Kharin YuS, Siarheeu AI, Arlou AA. On statistical testing of random and pseudorandom sequences based on entropy functionals. In: Kharin YuS, editor. Computer data analysis and modeling: stochastics and data science. Proceedings of the 13th International conference; 2022 September 6–10; Minsk, Belarus. Minsk: Belarusian State University; 2022. p. 148–162. EDN: QBMBVS.
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