A well-conditioned estimator for large-dimensional covariance matrices
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Ledoit-Wolf shrinkage computes the optimal shrinkage coefficient α by finding a bias-variance trade-off with no assumption on the data distribution.
“The optimal value of α is computed by finding a bias-variance trade-off with no assumption on the data distribution.”
From Signal Estimation and Uncertainties Extraction in Terahertz Time-Domain Spectroscopy (2025) · cites this paper as [55]
Section 2.2 describes the optimal shrinkage estimator as a trade-off between bias and variance, and Section 2.1 derives the optimal shrinkage weight. Section 2.1 says the method does not require a specific data distribution, but it does require finite fourth moments. Thus, the claim's unqualified statement that it makes no assumption on the data distribution is too broad. (LLM, conf=0.86)
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“A factor model can serve as the reference point for shrinkage estimation (see Ledoit and Wolf (2012) and Ledoit and Wolf (2004)).”
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“First, the covariance matrix can be inverted in low-dimensional settings (p n), but there can still be increased estimation errors when p approaches n (Ledoit & Wolf, 2004b).”
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Self-citationAnalytical nonlinear shrinkage of large-dimensional covariance matrices
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Self-citation
- Authors
- Ledoit, O., & Wolf, M.
- Affiliations
- University of California, Los Angeles (US)
- Universitat Pompeu Fabra (ES)
- Corresponding author
- Wolf, Michael
- Venue
- Journal of Multivariate Analysis
- Publisher
- Elsevier BV
- Published
- 2004-02
- Volume
- 88
- Issue
- 2
- Pages
- 365-411
- ISSN
- 0047-259X (ISSN-L)
- OpenAlex
- W2062125287
- Semantic Scholar
- b40890f3d917379ac4bd2e0933a134d45b4dc251
- Cited by
- 3,046
- References
- 24
- Citations by year
- 2026: 355 · 2025: 228 · 2024: 191 · 2023: 178 · 2022: 178 · 2021: 193 · 2020: 198 · 2019: 208 · 2018: 199 · 2017: 146 · 2016: 140 · 2015: 152 · 2014: 137 · 2013: 108 · 2012: 99
- FWCI
- 12.70
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Multivariate Analysis (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- e-Archivo (Carlos III University of Madrid) (submittedVersion, cc-by-nc-nd)
- Funders
- Yale University
- McDonnell Center for Systems Neuroscience
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- covariance matrix estimation, sample covariance matrix, convex combination, asymptotic optimality, squared error loss
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