Compound decisions and empirical Bayes via Bayesian nonparametrics
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915812402528256 |
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| author | Ignatiadis, Nikolaos Kankanala, Sid |
| author_facet | Ignatiadis, Nikolaos Kankanala, Sid |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compound decisions and empirical Bayes via Bayesian nonparametrics Ignatiadis, Nikolaos Kankanala, Sid Statistics Theory Econometrics Methodology 62C10, 62C12 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. |
| title | Compound decisions and empirical Bayes via Bayesian nonparametrics |
| topic | Statistics Theory Econometrics Methodology 62C10, 62C12 |
| url | https://arxiv.org/abs/2602.20115 |