We investigate the estimation of high-dimensional normal mean under sparsity. Most shrinkage priors in the literature are based on certain assumptions of sparsity levels and signal sizes. Violation of these assumptions can lead to unsatisfactory estimation. In this paper, we propose a new class of flexible priors, the adaptive normal-hypergeometric-inverted-Beta (ANHIB) priors, which generalize several popular shrinkage priors without requiring prior knowledge of data sparsity levels and signal sizes, and thus can be used as good default priors in a large variety of situations. We show that the ANHIB estimators provide strong suppression to noises and little shrinkage to large signals, and have consistently superior estimation performance under various sparsity levels and signal sizes.

中文翻译：

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稀疏信号的自适应正态超几何倒β先验

我们研究了稀疏下高维正态均值的估计。文献中的大多数收缩先验都是基于稀疏水平和信号大小的某些假设。违反这些假设可能会导致不令人满意的估计。在本文中，我们提出了一类新的灵活先验，自适应正态超几何倒置 Beta (ANHIB) 先验，它概括了几种流行的收缩先验，而不需要数据稀疏级别和信号大小的先验知识，因此可以使用在各种情况下作为良好的默认先验。我们表明，ANHIB 估计器对噪声有很强的抑制作用，对大信号的收缩很小，并且在各种稀疏级别和信号大小下始终具有出色的估计性能。