AI 中文总结
本文针对全局-局部先验，在放宽样本方差已知的假设、同时对误差方差赋予先验的情况下，推导收缩因子新尾界，给出目标参数后验均值的渐近极小极大速率。
AI 中文摘要
全局-局部先验（也常被称为收缩先验）已被证明是分析稀疏性高维数据的非常有效的工具，这类先验在不同场景下的渐近理论性质已在文献中得到研究，但据我们所知，目前这类先验的理论保证都包含样本方差已知的假设。本文放宽该假设，同时对误差方差也赋予先验进行分析，过程中推导了收缩因子的一些新尾界，并利用这些结果为目标参数的后验均值提供渐近极小极大速率。
英文摘要
Global-local priors, often also referred to as shrinkage priors, have proved to be a very effective tool for the analysis of high dimensional data under sparsity. Asymptotic theoretical properties of such priors, studied under various scenarios, are now available in the literature. However, to our knowledge, theoretical guarantees of such priors provided so far, involve the assumption of known sample variance. The present paper relaxes this assumption, and carries out the analysis with a prior assigned to the error variance as well. In the process, some new tail bounds for shrinkage factors are developed, and these results are then utilized in providing asymptotic minimax rates for the posterior means of the parameters of interest.
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