Title: New nonparametric estimation of entropy and applications
Authors: Issam El Hattab - ENCG-Casablanca, Hassan 2 University (Morocco) [presenting]
Abstract: The focus is on the nonparametric estimation of the Shannon's entropy and the some statistical tests. We introduce two new families of entropy estimators based on smooth quantile density estimators. The consistency and asymptotic normality of the proposed estimates are obtained. Our arguments, used to establish the asymptotic normality of our estimator, make use of an original application of the strong invariance principle for the uniform empirical process. A simulation study for the comparison, in terms of mean squared error, is performed, from which it follows that the proposed entropy estimates provides in this sense the most efficient approximation. Finally, we give some novel statistical tests based on our estimates.