标题： 经验贝叶斯，SURE和稀疏正态均值模型 显示英文标题

标题： Empirical Bayes, SURE and Sparse Normal Mean Models

摘要： 本文研究了在经验贝叶斯框架下的稀疏正态均值模型。 我们关注在零点有一个原子的混合先验和一个由最大化边缘似然或最小化Stein无偏风险估计确定的数据驱动位置为中心的密度成分。 我们研究了相应的后验中位数和后验均值的性质。 特别是，后验中位数是一个阈值规则，并具有多方向收缩特性，将观测值收缩到原点或数据驱动的位置。 通过考虑一个有限混合先验，该先验灵活地建模未知均值的聚类结构，扩展了这一想法。 我们将结果进一步推广到异方差正态均值模型。 具体而言，我们提出了一种半参数估计量，可以通过将熟悉的EM算法与用于等距回归的相邻违规者算法相结合来高效计算。 我们的方法的有效性通过广泛的数值研究得到了证明。 显示英文摘要

摘要： This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal likelihood or minimizing the Stein Unbiased Risk Estimate. We study the properties of the corresponding posterior median and posterior mean. In particular, the posterior median is a thresholding rule and enjoys the multi-direction shrinkage property that shrinks the observation toward either the origin or the data-driven location. The idea is extended by considering a finite mixture prior, which is flexible to model the cluster structure of the unknown means. We further generalize the results to heteroscedastic normal mean models. Specifically, we propose a semiparametric estimator which can be calculated efficiently by combining the familiar EM algorithm with the Pool-Adjacent-Violators algorithm for isotonic regression. The effectiveness of our methods is demonstrated via extensive numerical studies.