arXiv subjects

Benoit Oriol

Publications and source records attributed to Benoit Oriol.

5 recordsLinked to original sources

arXiv2024

Asymptotic spectrum of weighted sample covariance: another proof of spectrum convergence

We propose another proof of the high dimensional spectrum convergence of the weighted sample covariance, more concise and self-sufficient but with stronger, but reasonable assumptions. We explain and illustrates this theorem for different weight distributions and show how the spectrum behaves in finite samples with heavy tails. The general purpose is to provide a detailed introduction to the high dimensional spectrum of weighted sample covariance.

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arXiv2024

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 \textit{WeSpeR} algorithm and significantly speed up non-linear shrinkage in dimension higher than $1000$. Empirical tests confirm the good properties of the \textit{WeSpeR} algorithm. We provide the implementation in PyTorch for it.

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arXiv2024

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

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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arXiv2024

Analysis of a multi-target linear shrinkage covariance estimator

Multi-target linear shrinkage is an extension of the standard single-target linear shrinkage for covariance estimation. We combine several constant matrices - the targets - with the sample covariance matrix. We derive the oracle and a \textit{bona fide} multi-target linear shrinkage estimator with exact and empirical mean. In both settings, we proved its convergence towards the oracle under Kolmogorov asymptotics. Finally, we show empirically that it outperforms other standard estimators in various situations.

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arXiv2023

Ledoit-Wolf linear shrinkage with unknown mean

This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov asymptotics. When the mean is known, Ledoit and Wolf (2004) proposed a linear shrinkage estimator and proved its convergence under those asymptotics. To the best of our knowledge, no formal proof has been proposed when the mean is unknown. To address this issue, we propose to extend the linear shrinkage and its convergence properties to translation-invariant estimators. We expose four estimators respecting those conditions, proving their properties. Finally, we show empirically that a new estimator we propose outperforms other standard estimators.

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