OPTIMAL CLEANING FOR SINGULAR VALUES OF CROSS-COVARIANCE MATRICES

• 成果类型: Article
• 署名作者: Benaych-Georges, Florent; Bouchaud, Jean-Philippe; Potters, Marc
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1842
• 发表日期: 2023
• 页码: 1095-1126
• 关键词: eigenvectors; estimator

摘要

We give a new algorithm for the estimation of the cross-covariance ma-trix EXY' of two large-dimensional signals X e Rn, Y e Rp in the context where the number T of observations of the pair (X, Y) is large but n/T and p/ T are not supposed to be small. In the asymptotic regime where n, p, T are large, with high probability, this algorithm is optimal for the Frobenius norm among rotationally invariant estimators, that is, estimators derived from the empirical estimator by cleaning the singular values, while letting singular vectors unchanged.