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. 
Salim Bouzebda, Issam Elhattab, Amor Keziou and Tewfik Lounis
math.ST stat.TH