Rate of convergence of the nearest neighbor entropy estimator

The nearest neighbor entropy estimator was previously shown to converge for a broad class of stationary ergodic measures. In this paper, it is established that the estimator converges at a rate slower than O(1/logn)O(1/logn), where n is the number of observations. For the class of the symmetric Bernoulli measures an explicit formulae (see (7)) for the estimator's bias is obtained.1