# Optimal empirical Bayes estimation for the Poisson model via minimum-distance methods

arXiv: https://arxiv.org/abs/2209.01328 · HTML: https://mlsanity.com/paper/2209.01328/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2022.

## Built on by (most cited first, 5 of 5)

- [Solving Empirical Bayes via Transformers](https://mlsanity.com/paper/2502.09844/) (2025)
- [A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression](https://mlsanity.com/paper/2309.16843/) (2023)
- [Universal priors: solving empirical Bayes via Bayesian inference and pretraining](https://mlsanity.com/paper/2602.15136/) (2026)
- [Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problem](https://mlsanity.com/paper/2411.07651/) (2024)
- [Density estimation for Hellinger via minimum-distance estimators: mixtures of Gaussians, log-concave, and more](https://mlsanity.com/paper/2606.11469/) (2026)

## Abstract (arXiv)

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 the 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.