Principal components in linear mixed models with general bulk
研究了高维多元线性混合模型中协方差估计的主成分，发现主特征值和特征向量存在低维情形没有的偏差和混叠效应，推导了其极限行为，并发展了自由概率分析工具。
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 extending previous results from a more restrictive spiked model. Our analysis uses free probability techniques, and we develop two general tools of independent interest—strong asymptotic freeness of GOE and deterministic matrices and a free deterministic equivalent approximation for bilinear forms of resolvents.