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Ledoit-Wolf linear shrinkage with unknown mean

Oriol, Benoît; Miot, Alexandre (2023), Ledoit-Wolf linear shrinkage with unknown mean. https://basepub.dauphine.psl.eu/handle/123456789/24890

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Type
Document de travail / Working paper
External document link
https://hal.science/hal-04071051
Date
2023
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
50
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Author(s)
Oriol, Benoît
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Miot, Alexandre
Société Générale
Abstract (EN)
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.
Subjects / Keywords
covariance matrix estimation linear shrinkage Ledoit-Wolf estimator unknown mean general asymptotics; covariance matrix estimation; linear shrinkage; Ledoit-Wolf estimator; unknown mean; general asymptotics