Principal components in linear mixed models with general bulk

We study the principal components of covariance estimators in multivariate mixed-effects linear models. show that, high dimensions, eigenvalues and eigenvectors may exhibit bias aliasing effects that are not present low-dimensional settings. derive first-order limits eigenvalue locations eigenvector projections a high-dimensional asymptotic framework, allowing for general population spectral distributions random extending previous results from more restrictive spiked model. Our analysis uses free probability techniques, we develop two tools independent interest—strong freeness GOE deterministic matrices equivalent approximation bilinear forms resolvents.