Optimal cleaning for singular values of cross-covariance matrices

22 January 2019

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We give a new algorithm for the estimation of the cross-covariance matrix of two large dimensional signals X, Y in the context where the number T of observations of the pair (X,Y) is itself large, but with dimensions of X and Y non negligible with respect to T. This algorithm is optimal among rotationally invariant estimators, i.e. estimators derived from the empirical estimator by cleaning the singular values, while letting singular vectors unchanged. We give an interpretation of the singular value cleaning in terms of overfitting ratios.

Authors

Florent Benaych-Georges , Jean-Philippe Bouchaud , Marc Potters