# A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family

arXiv: https://arxiv.org/abs/1910.08997 · HTML: https://mlsanity.com/paper/1910.08997/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2019.

## Built on by (most cited first, 2 of 2)

- [Empirical Bayes Estimation with Side Information: A Nonparametric Integrative Tweedie Approach](https://mlsanity.com/paper/2308.05883/) (2023)
- [Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problem](https://mlsanity.com/paper/2411.07651/) (2024)

## Abstract (arXiv)

We develop a Nonparametric Empirical Bayes (NEB) framework for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We propose to directly estimate the Bayes shrinkage factor in the generalized Robbins' formula via solving a scalable convex program, which is carefully developed based on a RKHS representation of the Stein's discrepancy measure. The new NEB estimation framework is flexible for incorporating various structural constraints into the data driven rule, and provides a unified approach to compound estimation with both regular and scaled squared error losses. We develop theory to show that the class of NEB estimators enjoys strong asymptotic properties. Comprehensive simulation studies as well as analyses of real data examples are carried out to demonstrate the superiority of the NEB estimator over competing methods.