Entropy estimation in Turing's perspective (Q2919410)

In this paper, the author studies the entropy estimator \({\hat H}_z\) which is defined by the arithmetic mean on \(\nu\) for \(\sum_k p_k(1-p_k)^{\nu}\). As main results, a few lemmas and theorems are shown.NEWLINENEWLINE In Lemma 1, the author gives a necessary and sufficient condition for the entropy \(H\) to be finite. In Lemma 2 he gives an upper bound for the variance of the entropy estimator \({\hat H}_z\), and then shows that the entropy estimator \({\hat H}_z\) is a consistent estimator of the entropy \(H\) under the condition that \(H\) is finite (Theorem 1). Using Lemma 2, the author obtains another important theorem, Theorem 2. Examples and remarks are given. Finally, computational results are given and compared with those of other estimators.