Estimating eigenvectors and eigenspaces of covariance matrices: Optimal Bounds and Conditions for Consistency

Phuc Tran, Van Vu

Let $X=[\hat{I}{¾}_1,\hat{I}{¾}_2,...,\hat{I}{¾}_d{]}^{\top }$ be a zero-mean random vector of large dimension $d$ ($d\to \infty$) with (hidden) covariance matrix $M = (m_{ij})_{1 \leq i…