An NPMLE-based empirical Bayes estimator is shown to be competitively optimal (up to log factors) for KL-risk distribution estimation, while Good-Turing is provably suboptimal.
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Besting Good--Turing: Optimality of Non-Parametric Maximum Likelihood for Distribution Estimation
An NPMLE-based empirical Bayes estimator is shown to be competitively optimal (up to log factors) for KL-risk distribution estimation, while Good-Turing is provably suboptimal.