Principal components in linear mixed models with general bulk
Principal components in linear mixed models with general bulk
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DOI：
10.1214/20-aos2010
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发表时间：
2019-03
期刊：
影响因子：
--
通讯作者：
Z. Fan;Yi Sun;Zhichao Wang
中科院分区：
文献类型：
--
作者：
Z. Fan;Yi Sun;Zhichao Wang
我们研究多元混合效应线性模型中协方差估计量的主成分。我们表明，在高维情况下，主特征值和特征向量可能会表现出在低维设定中不存在的偏差和混叠效应。我们在高维渐近框架下推导了主特征值位置和特征向量投影的一阶极限，考虑了随机效应的一般总体谱分布，并扩展了来自更具限制性的尖峰模型的先前结果。我们的分析使用了自由概率技术，并且我们开发了两个具有独立研究价值的通用工具——高斯正交系综（GOE）与确定性矩阵的强渐近自由性以及预解式双线性形式的自由确定性等价逼近。
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.