Minimax Rate-optimal Estimation of KL Divergence between Discrete Distributions.

We refine the general methodology in [1] for the construction and analysis of essentially minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions with support size comparable with the number of observations . Specifically, we determine the "smooth" and "non-smooth" regimes based on the confidence set and the smoothness of the functional. In the "non-smooth" regime, we apply an unbiased estimator for a "suitable" polynomial approximation of the functional.

Minimax Estimation of Functionals of Discrete Distributions.

We propose a general methodology for the construction and analysis of essentially minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the support size is unknown and may be comparable with or even much larger than the number of observations . We treat the respective regions where the functional is nonsmooth and smooth separately. In the nonsmooth regime, we apply an unbiased estimator for the best polynomial approximation of the functional whereas, in the smooth regime, we apply a bias-corrected version of the maximum likelihood estimator (MLE).