论文标题
使用Ledoit-Wolf非线性收缩估算器对Hotelling $ T^2 $测试的改进
An Improvement on the Hotelling $T^2$ Test Using the Ledoit-Wolf Nonlinear Shrinkage Estimator
论文作者
论文摘要
Hotelling的$ T^2 $测试是一种经典的方法，用于区分共享人口协方差矩阵的两个多元普通样本的平均值。 Hotelling的测试对于高维样品而言并不理想，因为估计的样品协方差矩阵的特征值是其人口对应物的不一致的估计器。 We replace the sample covariance matrix with the nonlinear shrinkage estimator of Ledoit and Wolf 2020. We observe empirically for sub-Gaussian data that the resulting algorithm dominates past methods (Bai and Saranadasa 1996, Chen and Qin 2010, and Li et al. 2020) for a family of population covariance matrices that includes matrices with high or low condition number and many or few nontrivial --即，尖峰 - 特征值。
Hotelling's $T^2$ test is a classical approach for discriminating the means of two multivariate normal samples that share a population covariance matrix. Hotelling's test is not ideal for high-dimensional samples because the eigenvalues of the estimated sample covariance matrix are inconsistent estimators for their population counterparts. We replace the sample covariance matrix with the nonlinear shrinkage estimator of Ledoit and Wolf 2020. We observe empirically for sub-Gaussian data that the resulting algorithm dominates past methods (Bai and Saranadasa 1996, Chen and Qin 2010, and Li et al. 2020) for a family of population covariance matrices that includes matrices with high or low condition number and many or few nontrivial -- i.e., spiked -- eigenvalues.
