On Convergence Rates of Spiked Eigenvalue Estimates: A General Study of Global and Local Laws in Sample Covariance Matrices
By: Bing-Yi Jing , Weiming Li , Jiahui Xie and more
Potential Business Impact:
Finds patterns in data with changing sizes.
This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio $M/N$ can approach zero, a constant, or infinity. These theories are utilized to determine the convergence rate of spiked eigenvalue estimates.
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