PRINCIPAL COMPONENTS IN LINEAR MIXED MODELS WITH GENERAL BULK

• 成果类型: Article
• 署名作者: Fan, Zhou; Sun, Yi; Wang, Zhichao
• 署名单位: Yale University; University of Chicago; University of California System; University of California San Diego
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2010
• 发表日期: 2021
• 页码: 1489-1513
• 关键词: sample autocovariance matrices; asymptotic freeness; LARGEST EIGENVALUE; genetic variance; POLYNOMIALS; expression; Respect; wigner

摘要

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.