An asymptotic lower bound for the entropy of discrete populations with application to the estimation of entropy for approximately uniform populations (Q2525494)

The authors derive under certain restrictions on the underlying multinomial population an asymptotic lower bound for the Shannon entropy \(H\) and propose to use this bound as an estimator of the entropy in place of the maximum likelihood estimator \(\hat H\). For (discrete) uniform populations some numerical results are given which show the superiority of the proposed estimator over the maximum likelihood one. (The authors do not refer to \textit{G. P. Basharin}'s paper [Teor. Veroyatn. Primen. 4, 361--364 (1959; Zbl 0092.36701)] where some properties of the maximum likelihood estimator \(\hat H\) are investigated and do not discuss the similar properties of their estimator.)