ANALYTICAL NONLINEAR SHRINKAGE OF LARGE-DIMENSIONAL COVARIANCE MATRICES

• 成果类型: Article
• 署名作者: Ledoit, Olivier; Wolf, Michael
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1921
• 发表日期: 2020
• 页码: 3043-3065
• 关键词: limiting spectral distribution; Empirical distribution; eigenvalues

摘要

This paper establishes the first analytical formula for nonlinear shrinkage estimation of large-dimensional covariancematrices. We achieve this by identifying and mathematically exploiting a deep connection between nonlinear shrinkage and nonparametric estimation of the Hilbert transform of the sample spectral density. Previous nonlinear shrinkage methods were of numerical nature: QuEST requires numerical inversion of a complex equation from random matrix theory whereas NERCOME is based on a sample-splitting scheme. The new analytical method is more elegant and also has more potential to accommodate future variations or extensions. Immediate benefits are (i) that it is typically 1000 times faster with basically the same accuracy as QuEST and (ii) that it accommodates covariance matrices of dimension up to 10,000 and more. The difficult case where the matrix dimension exceeds the sample size is also covered.