# Quasi-Bayes empirical Bayes estimation of sums of random variables

arXiv: https://arxiv.org/abs/2606.21707 · HTML: https://mlsanity.com/paper/2606.21707/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2026.

## Built on by (most cited first, 1 of 1)

- [Poisson empirical Bayes estimation of sums of random variables via minimum-distance methods](https://mlsanity.com/paper/2610.07190/) (2026)

## Abstract (arXiv)

The estimation of sums of functions of observable and unobservable variables is a long-standing problem in statistics with applications across many domains. Empirical Bayes methods provide a natural framework for this task under mixture models, but existing approaches often rely on restrictive parametric assumptions or apply only to limited classes of functionals in nonparametric settings. We propose a nonparametric methodology, referred to as quasi-Bayes empirical Bayes, that addresses these limitations through a recursive estimation of the mixing distribution based on Newton's algorithm. The resulting plug-in estimate of the target sum is computationally efficient, scalable, and applicable to a broad class of utility functions, while enabling uncertainty quantification via asymptotic credible intervals derived from a Gaussian central limit theorem. We establish large sample asymptotic theoretical guarantees by proving a merging between the quasi-Bayes and Bayes estimates and by showing consistency under a correctly specified frequentist model. Synthetic-data and real-data analyses demonstrate the practical accuracy and stability of the method, with performance comparable to, and in some cases better than, existing empirical Bayes procedures.