PCA and eigen-inference for a spiked covariance model with largest eigenvalues of same asymptotic order

Chi-Square Approximation for the Distribution of Individual Eigenvalues of a Singular Wishart Matrix

“…In the context of the High Dimension-Low Sample Size (HDLSS) setting, the asymptotic behavior of the eigenvalue distribution of a sample covariance matrix was discussed in Ahn et al [18], Bolivar-Cime and Perez-Abreu [19], Jung and Marron [20]. Jung and Marron [20] showed that the spiked sample eigenvalues are approximated by the chi-square distribution with a degree of freedom of n. In contrast, Theorem 1 provides the approximation of the distribution of individual eigenvalues by a chi-square distribution with varying degrees of freedom.…”