大尺度结构协方差的非线性收缩估计
Non-linear shrinkage estimation of large-scale structure covariance
摘要：
在许多天体物理学环境中，大型数据集的协方差矩阵必须从有限数量的模拟实现中凭经验确定。由此产生的噪声降低了推理，如果实现比数据点少，则完全排除了推理。这项工作适用于最近提出的非线性收缩估计的协方差从大尺度结构宇宙学的一个现实的例子。在优化其性能的使用在似然表达式，收缩估计量产生次显性偏差和方差可比的标准估计因子$\sim 50$少实现。这是在没有任何关于数据属性或协方差矩阵结构的先验信息的情况下实现的，计算成本可以忽略不计。
英文摘要：
In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer realisations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimising its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor $\sim 50$ less realisations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at negligible computational cost.
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