WeSpeR: Computing non-linear shrinkage formulas for the weighted sample covariance

We address the issue of computing the non-linear shrinkage formulas for the weighted sample covariance in high dimension. We use theoretical properties of the asymptotic sample spectrum in order to derive the $\mathit{\text{WeSpeR}}$ algorithm and significantly speed up non-linear shrinkage in dimension higher than $1000$. Empirical tests confirm the good properties of the $\mathit{\text{WeSpeR}}$ algorithm. We provide the implementation in PyTorch for it.