Optimal cleaning for singular values of cross-covariance matrices
We give a new algorithm for the estimation of the cross-covariance matrix E XY' of two large dimensional signals X ∊ Rn, Y ∊ Rpin the context where the number T of observations of the pair (X,Y) is itself large, but with T ⋡ n,p. 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.