Uniform-in-bandwidth consistency for kernel-type estimators of Shannon's entropy

We establish uniform-in-bandwidth consistency for kernel-type estimators of the differential entropy. We consider two kernel-type estimators of Shannon's entropy. As a consequence, an asymptotic 100% confidence interval of entropy is provided

New Entropy Estimator with an Application to Test of Normality

In the present paper we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed