Nikolaos Ignatiadis, Sid Kankanala
arXiv 23 Feb 2026 · Mathematics — Statistics Theory
arXiv:2602.20115 · PDF · DOI · OpenAlex · Extracted main text
We study the Gaussian sequence compound decision problem and analyze a Bayesian nonparametric estimator from an empirical Bayes, regret-based perspective. Motivated by sharp results for the classical nonparametric maximum likelihood estimator (NPMLE), we ask whether an analogous guarantee can be obtained using a standard Bayesian nonparametric prior. We show that a Dirichlet-process-based Bayesian procedure achieves near-optimal regret bounds. Our main results are stated in the compound decision framework, where the mean vector is treated as fixed, while we also provide parallel guarantees under a hierarchical model in which the means are drawn from a true unknown prior distribution. The posterior mean Bayes rule is, a fortiori, admissible, whereas we show that the NPMLE plug-in rule is inadmissible.
appendix boundary found by appendix_command · 50% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Jiang, Wenhua and Zhang, Cun-Hui (2009) General Maximum Likelihood Empirical Bayes Estimation of Normal Means | 0.946 | 13 | 6 | 85% |
| 2 | Datta, Somnath (1991) Asymptotic Optimality of Bayes Compound Estimators in Compact Exponential Families | 0.843 | 3 | 3 | 100% |
| 3 | Robbins, Herbert (1951) Asymptotically Subminimax Solutions of Compound Statistical Decision Problems | 0.843 | 3 | 3 | 100% |
| 4 | Ghosal, Subhashis and van der Vaart, Aad W (2001) Entropies and Rates of Convergence for Maximum Likelihood and Bayes Estimation for Mixtures of Normal Densities | 0.737 | 3 | 3 | 67% |
| 5 | Cannella, Nick and Teh, Anzo and Han, Yanjun and Polyanskiy, Yury (2026) Universal Priors: Solving Empirical Bayes via Bayesian Inference and Pretraining | 0.737 | 3 | 2 | 100% |
| 6 | Efron, Bradley (2019) Bayes, Oracle Bayes and Empirical Bayes | 0.737 | 3 | 2 | 100% |
| 7 | Robbins, Herbert (1956) An Empirical Bayes Approach to Statistics | 0.737 | 3 | 2 | 100% |
| 8 | Efron, Bradley (2014) Two Modeling Strategies for Empirical Bayes Estimation | 0.644 | 2 | 2 | 100% |
| 9 | Escobar, Michael D. and West, Mike (1995) Bayesian Density Estimation and Inference Using Mixtures | 0.644 | 2 | 2 | 100% |
| 10 | Good, I. J (1992) The Bayes/Non-Bayes Compromise: A Brief Review | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 78 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Sharp regret–Hellinger bounds for Gaussian empirical Bayes via polynomial approximation | 0.405 | 1 | 1 |