  KSG mutual information estimator, which is based on the distances of each
sample to its k-th nearest neighbor, is widely used to estimate mutual
information between two continuous random variables. Existing work has analyzed
the convergence rate of this estimator for random variables whose densities are
bounded away from zero in its support. In practice, however, KSG estimator also
performs well for a much broader class of distributions, including not only
those with bounded support and densities bounded away from zero, but also those
with bounded support but densities approaching zero, and those with unbounded
support. In this paper, we analyze the convergence rate of the error of KSG
estimator for smooth distributions, whose support of density can be both
bounded and unbounded. As KSG mutual information estimator can be viewed as an
adaptive recombination of KL entropy estimators, in our analysis, we also
provide convergence analysis of KL entropy estimator for a broad class of
distributions.
