Nonparametric estimation of quantile-based entropy function

Abstract

In this article, we propose three nonparametric estimators for quantile-based Shannon differential entropy function for complete samples. Asymptotic properties of the estimators are established under suitable regularity conditions. Simulation study are carried out to compare the performance of the proposed estimators and with other important entropy estimators. The usefulness of the new estimators are also illustrated using real data sets.

Keywords:

• Kernel density estimation
• mean squared error
• quantile function
• Shannon differential entropy function

2010 Mathematical Subject Classification:

• 94A17
• 62G07

Acknowledgements

The second, third and the fourth authors would like to thank the support of the University Grants Commission, India, under the Special Assistance Programme. The authors wish to thank the referees for their constructive comments.