协方差矩阵的Ledoit-Péché RIE公式的一个简短证明

加权样本协方差的渐近非线性收缩与特征向量重叠

Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance

该研究推导了加权样本协方差的渐近非线性收缩公式及特征向量重叠分布，给出指数加权情形的具体公式与数值算法，验证了估计量性能与理论对重尾分布的鲁棒性。

分层黎曼空间上的几何状态切换扩散及其在协方差矩阵中的应用

Geometric Regime--Switching Diffusions on Stratified Riemannian Spaces with an Application to Covariance Matrices

研究构建分层黎曼空间上的几何状态切换扩散，通过鞅问题刻画，结合泊松稀疏机制构建过程并证明唯一性，应用于协方差矩阵锥，得到 \(V\)-均匀几何遍历过程。

Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices

Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance matrices). While the potential applications of such models have attracted significant attention, a major obstacle still stands in the way of these applications: there seems to exist no practical method of computing the normalising factors associated with Riemannian Gaussian distributions on spaces of high-dimensional covariance matrices. The present paper shows that …

大协方差矩阵的估计：自由反卷积的计算与统计方面

Estimation of large covariance matrices via free deconvolution: computational and statistical aspects

本文利用自由概率论中的自由反卷积方法，通过复分析求$S$-变换的逆，解决大协方差矩阵估计的高维偏差问题，并兼顾计算与统计方面。