The paper addresses asymptotic estimation of normal means under sparsity. The primary focus is estimation of multivariate normal means where we obtain exact asymptotic minimax error under global-local shrinkage prior. This extends the corresponding univariate work of Ghosh and Chakrabarti (2017). In addition, we obtain similar results for the Dirichlet-Laplace prior as considered in Bhattacharya, Pati, Pillai, and Dunson (2015). Also, following van der Pas, Szabo, and van der Vaart (2017), we have been able to derive credible sets for multivariate normal means under global-local priors.

翻译：本文研究了稀疏性下正态均值的渐近估计问题。主要关注在全局-局部收缩先验下，多元正态均值的精确渐近极小化误差估计。该工作扩展了Ghosh和Chakrabarti（2017）在单变量情形下的相关研究。此外，我们针对Bhattacharya、Pati、Pillai和Dunson（2015）提出的Dirichlet-Laplace先验获得了类似结果。同时，借鉴van der Pas、Szabo和van der Vaart（2017）的研究，我们推导出了全局-局部先验下多元正态均值的可信集。