Principal components in linear mixed models with general bulk

@article{Fan2019PrincipalCI,
  title={Principal components in linear mixed models with general bulk},
  author={Zhou Fan and Yi Sun and Zhichao Wang},
  journal={arXiv: Probability},
  year={2019}
}
We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present in low-dimensional settings. We derive the first-order limits of the principal eigenvalue locations and eigenvector projections in a high-dimensional asymptotic framework, allowing for general population spectral distributions for the random effects and… 

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