Nonparametric estimation of the entropy using a ranked set sample. (English) Zbl 1391.94583
Summary: This article is concerned with nonparametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random sampling. The applications of the proposed estimator to the mutual information estimation as well as estimation of the Kullback-Leibler divergence are provided. Several Monté-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 datasets to illustrate applicability of theoretical results.
MSC:
| 94A17 | Measures of information, entropy |
| 62D05 | Sampling theory, sample surveys |
| 62G07 | Density estimation |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
kernel density estimation; multi-stage ranked set sampling; nonlinear dependency; optimal bandwidth selectionReferences:
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