Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices

  title={Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices},
  author={T. Tony Cai and Xiao Han and Guangming Pan},
  journal={The Annals of Statistics},
We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are bounded but otherwise arbitrary. The limiting normal distribution for the spiked sample eigenvalues is established. It has distinct features that the asymptotic mean relies on not only the population spikes but also the nonspikes and that the asymptotic… Expand

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