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.

翻译：本文研究高斯序列复合决策问题，并从经验贝叶斯与遗憾度视角分析一种贝叶斯非参数估计量。受经典非参数最大似然估计量（NPMLE）精确结果的启发，我们探讨能否通过标准贝叶斯非参数先验获得类似的理论保证。研究表明，基于狄利克雷过程的贝叶斯方法能够达到近乎最优的遗憾度界。主要结论在复合决策框架下建立（其中均值向量被视为固定参数），同时我们在分层模型下给出并行理论保证（该模型中均值从真实未知先验分布中抽取）。后验均值贝叶斯决策规则具有容许性，而本文证明NPMLE插件规则是非容许的。