Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter assessment. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.

中文翻译：

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用于正则化参数评估的光谱条件数图

许多现代统计应用要求在变量数量大于观察数量的设置中估计协方差（或精度）矩阵。存在大量的山脊型估计器，它们使用正则化来应对样本协方差矩阵的后续奇异性。这些估计器取决于惩罚参数，并且就其计算上的可行性或仅对于受限的一组岭型估计器而言难以成立，就很难选择其值。在这里，我们介绍了一个简单的图形工具，即光谱条件数图，用于进行启发式惩罚参数评估。所提出的工具在计算上是友好的，并且可以用于所有类型的岭型协方差（精度）估计量。