A Bayesian nonparametric estimator to entropy is proposed. The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (Journal of Royal Statistical Society B 38 (1976) 54–59) and Ebrahimi, Pflughoeft and Soofi (Statistics & Probability Letters 20 (1994) 225–234). Several theoretical properties, such as consistency, of the proposed estimator are obtained. The quality of the proposed estimator has been investigated through several examples, in which it exhibits excellent performance.
The authors are grateful to the Editor, the Associate Editor and the reviewer for their comments and suggestions that have greatly improved the paper.
"A Bayesian nonparametric estimation to entropy." Braz. J. Probab. Stat. 35 (2) 421 - 434, May 2021. https://doi.org/10.1214/20-BJPS483