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

Benoit Oriol

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arXiv · 2410.14420

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

Benoit Oriol

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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.

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Benoit Oriol. 2024-10-18. Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance. https://arxiv.org/abs/2410.14420

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