On the Distribution of the Largest Eigenvalue in Principal Components Analysis

Abstract

Stanford University Let x 1 denote the square of the largest singular value of an n × 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… (More)

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