Nonparametric estimation of the entropy using a ranked set sample

This paper is concerned with kernel-based estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied and compared with those of the rival estimator in simple random sampling. The applications of the proposed estimator to the mutual information estimation as well as the goodness of fit testing are provided. Several Monte-Carlo simulation studies are conducted to examine the performance of the estimator. The results are applied to the longleaf pine (pinus palustris) trees and the body fat percentage data sets to illustrate applicability of theoretical results.