Ledoit-Wolf linear shrinkage with unknown mean

• URL: http://arxiv.org/abs/2304.07045v1
• Date: Fri, 14 Apr 2023 10:40:30 GMT
• Title: Ledoit-Wolf linear shrinkage with unknown mean
• Authors: Benoit Oriol and Alexandre Miot
• Abstract summary: This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical quadratic covariance estimator fails when dimension and number of samples are proportional and tend to infinity. We propose a new estimator and prove its convergence under the Ledoit and Wolf assumptions.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 a new estimator and prove its quadratic convergence under the Ledoit and Wolf assumptions. Finally, we show empirically that it outperforms other standard estimators.

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