  Estimating Kullback-Leibler divergence from identical and independently
distributed samples is an important problem in various domains. One simple and
effective estimator is based on the k nearest neighbor distances between these
samples. In this paper, we analyze the convergence rates of the bias and
variance of this estimator. Furthermore, we derive a lower bound of the minimax
mean square error and show that kNN method is asymptotically rate optimal.
