Eigenvector overlaps in large sample covariance matrices and nonlinear
shrinkage estimators
Eigenvector overlaps in large sample covariance matrices and nonlinear
shrinkage estimators
Consider a data matrix $Y = [\mathbf{y}_1, \cdots, \mathbf{y}_N]$ of size $M \times N$, where the columns are independent observations from a random vector $\mathbf{y}$ with zero mean and population covariance $\Sigma$. Let $\mathbf{u}_i$ and $\mathbf{v}_j$ denote the left and right singular vectors of $Y$, respectively. This study investigates the …