# Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance

arXiv: https://arxiv.org/abs/2410.14420 · HTML: https://mlsanity.com/paper/2410.14420/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2024.

## Abstract (arXiv)

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 P'ech'e. 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.