# 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} }

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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