TRACY-WIDOM AT EACH EDGE OF REAL COVARIANCE AND MANOVA ESTIMATORS

• 成果类型: Article
• 署名作者: Fan, Zhou; Johnstone, Iain M.
• 署名单位: Yale University; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1754
• 发表日期: 2022
• 页码: 2967-3003
• 关键词: limiting spectral distribution; LARGEST EIGENVALUE; Empirical distribution; UNIVERSALITY; matrices; fluctuations; variance

摘要

We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix dimensions increase proportionally, the asymptotic spectra of such estimators may have multiple disjoint intervals of support, possibly intersecting the negative half line. We show that the distribution of the extremal eigenvalue at each regular edge of the support has a GOE Tracy-Widom limit. Our proof extends a comparison argument of Ji Oon Lee and Kevin Schnelli, replacing a continuous Green function flow by a discrete Lindeberg swapping scheme.