On the choice of nonparametric entropy estimator in entropy-based goodness-of-fit test statistics

Entropy-based goodness-of-fit test statistics can be established by estimating the entropy difference or Kullback-Leibler information, and several entropy-based test statistics based on various entropy estimators have been proposed. In this article, we first give comments on some problems resulting from not satisfying the moment constraints. We then study the choice of the entropy estimator by noting the reason why a test based on a better entropy estimator does not necessarily provide better powers.