OPTIMAL CLEANING FOR SINGULAR VALUES OF CROSS-COVARIANCE MATRICES

被引：3

作者：

Benaych-Georges, Florent ^{[1
]}

Bouchaud, Jean-Philippe ^{[1
]}

Potters, Marc ^{[1
]}

机构：

[1] CFM, Cincinnati, OH 45215 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 02期

关键词：

Random matrices; cross-covariance matrices; rotationally invariant estimator; EIGENVECTORS; ESTIMATOR;

D O I：

10.1214/22-AAP1842

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1095 / 1126

页数：32

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