论文标题
在收缩中放松高斯假设并确保高维度
Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension
论文作者
论文摘要
收缩估计是现代统计数据的基本工具，由查尔斯·斯坦（Charles Stein）发现涉及多元高斯的著名悖论时，他率先进行。随后的很大一部分文献只考虑了收缩效率，以及在该原始工作的高斯环境中被称为斯坦的无偏风险估计的相关程序。我们研究了收缩有效性领域的扩展，并可以通过使用现在称为Stein方法的概率区域中开发的工具来远离高斯。我们表明，在非常温和的条件下，收缩率有效地远离高斯的噪声分布。当然，在类似的假设下，尤其是在保留了Pinsker定理的经典渐近学的方式下，也被证明是适应性的。值得注意的是，在温和的分布假设下，特别是对于一般的各向同性对数洞穴测量，收缩和肯定是有效的。
Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known as Stein's Unbiased Risk Estimate, or SURE, in the Gaussian setting of that original work. We investigate what extensions to the domain of validity of shrinkage and SURE can be made away from the Gaussian through the use of tools developed in the probabilistic area now known as Stein's method. We show that shrinkage is efficient away from the Gaussian under very mild conditions on the distribution of the noise. SURE is also proved to be adaptive under similar assumptions, and in particular in a way that retains the classical asymptotics of Pinsker's theorem. Notably, shrinkage and SURE are shown to be efficient under mild distributional assumptions, and particularly for general isotropic log-concave measures.
