MSE Comparison of Some Different Estimators of Entropy.

The present paper is motivated by the work of Kozachenko and Leonenko (Kozachenko, L. F., Leonenko, N. N. (1987). On statistical estimation of entropy of random vector. Problems Infor. Transmiss. 23:9-16) where a new estimator of entropy is proposed. Here we reformulate it in terms of spacings of order m and we compare the mean square error (MSE) of the reformulated estimator with those of three alternative competitors, introduced in literature by Vasicek (Vasicek, O. (1976). A test of normality based on sample entropy. J. Roy. Stat. Soc., Ser. B 38:254-256), and more recently by van Es (van Es, B. (1992). Estimating functionals related to a density by class of statistics based on spacing. Scand. J. Statist. 19:61-72) and Correa (Correa, J. C. (1995). A new estimator of entropy. Commun. Statist.--Theory Meth. 24:2439-2449), respectively. [ABSTRACT FROM AUTHOR]