Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models.

Sample correlation matrices are widely used, but for high-dimensional data little is known about their spectral properties beyond "null models", which assume the data have independent coordinates. In the class of spiked models, we apply random matrix theory to derive asymptotic first-order and distributional results for both leading eigenvalues and eigenvectors of sample correlation matrices, assuming a high-dimensional regime in which the ratio , of number of variables to sample size , converges to a positive constant. While the first-order spectral properties of sample correlation matrices match those of sample covariance matrices, their asymptotic distributions can differ significantly.

EDGEWORTH CORRECTION FOR THE LARGEST EIGENVALUE IN A SPIKED PCA MODEL.

We study improved approximations to the distribution of the largest eigenvalue of the sample covariance matrix of zero-mean Gaussian observations in dimension + 1. We assume that one population principal component has variance ℓ > 1 and the remaining 'noise' components have common variance 1. In the high-dimensional limit 0, we study Edgeworth corrections to the limiting Gaussian distribution of in the supercritical case .