  The Robbins estimator is the most iconic and widely used procedure in the
empirical Bayes literature for the Poisson model. On one hand, this method has
been recently shown to be minimax optimal in terms of the regret (excess risk
over the Bayesian oracle that knows the true prior) for various nonparametric
classes of priors. On the other hand, it has been long recognized in practice
that Robbins estimator lacks the desired smoothness and monotonicity of Bayes
estimators and can be easily derailed by those data points that were rarely
observed before. Based on the minimum-distance distance method, we propose a
suite of empirical Bayes estimators, including the classical nonparametric
maximum likelihood, that outperform the Robbins method in a variety of
synthetic and real data sets and retain its optimality in terms of minimax
regret.
