  Wide conditions are provided to guarantee asymptotic unbiasedness and
L^2-consistency of the introduced estimates of the Kullback-Leibler divergence
for probability measures in R^d having densities w.r.t. the Lebesgue measure.
These estimates are constructed by means of two independent collections of
i.i.d. observations and involve the specified k-nearest neighbor statistics. In
particular, the established results are valid for estimates of the
Kullback-Leibler divergence between any two Gaussian measures in R^d with
nondegenerate covariance matrices. As a byproduct we obtain new statements
concerning the Kozachenko-Leonenko estimators of the Shannon differential
entropy.
