Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance
This work provides incremental improvements to covariance estimation methods, primarily benefiting statistical and machine learning applications in finance or signal processing.
The authors tackled the problem of estimating covariance and precision matrices for weighted sample covariances, deriving asymptotic non-linear shrinkage formulas and proposing a numerical algorithm, with experimental results showing performance improvements and robustness to heavy-tailed distributions.
We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and Péché. We detail explicitly the formulas for exponentially-weighted sample covariances. We propose an algorithm to numerically compute those formulas. Experimentally, we show the performance of the asymptotic non-linear shrinkage estimators. Finally, we test the robustness of the theory to a heavy-tailed distributions.