  In this research work, a total of 45 different estimators of the Shannon
differential entropy were reviewed. The estimators were mainly based on three
classes, namely: window size spacings, kernel density estimation (KDE) and
k-nearest neighbour (kNN) estimation. A total of 16, 5 and 6 estimators were
selected from each of the classes, respectively, for comparison. The
performances of the 27 selected estimators, in terms of their bias values and
root mean squared errors (RMSEs) as well as their asymptotic behaviours, were
compared through extensive Monte Carlo simulations. The empirical comparisons
were carried out at different sample sizes of 10, 50, and 100 and different
variable dimensions of 1, 2, 3, and 5, for three groups of continuous
distributions according to their symmetry and support. The results showed that
the spacings based estimators generally performed better than the estimators
from the other two classes at univariate level, but suffered from non existence
at multivariate level. The kNN based estimators were generally inferior to the
estimators from the other two classes considered but showed an advantage of
existence for all dimensions. Also, a new class of optimal window size was
obtained and sets of estimators were recommended for different groups of
distributions at different variable dimensions. Finally, the asymptotic biases,
variances and distributions of the 'best estimators' were considered.
