On the distribution of the largest eigenvalue in principal components analysis

@article{Johnstone2001OnTD,
  title={On the distribution of the largest eigenvalue in principal components analysis},
  author={Iain M. Johnstone},
  journal={Annals of Statistics},
  year={2001},
  volume={29},
  pages={295-327}
}
  • I. Johnstone
  • Published 1 April 2001
  • Mathematics
  • Annals of Statistics
Let x (1) denote the square of the largest singular value of an n x p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x (1) is the largest principal component variance of the covariance matrix X'X, or the largest eigenvalue of a p-variate Wishart distribution on n degrees of freedom with identity covariance. Consider the limit of large p and n with n/p = y ≥ 1. When centered by μ p = (√n-1 + √p) 2 and scaled by σ p = (√n-1 + √p)(1/√n-1 + 1/√p) 1/3 , the… 

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