A Gamma-smoothed NPMLE for Poisson empirical Bayes achieves optimal nearly parametric rates for posterior means and enables asymptotically exact, shorter marginal coverage confidence sets under compact support.
Sharp regret bounds for empirical Bayes and compound decision problems
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The paper proves sharp O(ε² log(1/ε)/log log(1/ε)) regret bounds for unregularized Bayes rules with compactly supported priors via polynomial approximation, improving on prior regularized results with extra log factors.
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Poisson Empirical Bayes via Gamma-Smoothed Nonparametric Maximum Likelihood
A Gamma-smoothed NPMLE for Poisson empirical Bayes achieves optimal nearly parametric rates for posterior means and enables asymptotically exact, shorter marginal coverage confidence sets under compact support.
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Sharp regret-Hellinger bounds for Gaussian empirical Bayes via polynomial approximation
The paper proves sharp O(ε² log(1/ε)/log log(1/ε)) regret bounds for unregularized Bayes rules with compactly supported priors via polynomial approximation, improving on prior regularized results with extra log factors.