Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance
Statistics Theory
2025-03-21 v2 Machine Learning
Probability
Applications
Machine Learning
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2410.14420,
title = {Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance},
author = {Benoit Oriol},
journal= {arXiv preprint arXiv:2410.14420},
year = {2025}
}