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A well-conditioned estimator for large-dimensional covariance matrices
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InfluentialThe minimum regularized covariance determinant estimator
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“, [17], [20]), here we compare with the empirically computed “oracle” solution, in which φ is chosen to minimize the normalized total output power in (6).”
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“Furthermore, several previous studies have compared the three linear shrinkage estimators of Ledoit and Wolf (2003, 2004a,b) without being able to find a clear winner among them; for example, see Ledoit and Wolf (2004a) and DeMiguel et al. (2009a).”
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“Firstly, they depend on the unknown covariance matrix (of the background surrounding the test pixel) whose entries have to be carefully estimated specially in large dimensions [21], [22], [23] and to ensure success under different environment [24], [25], [26].”
BackgroundNonparametric Stein-type shrinkage covariance matrix estimators in high-dimensional settings
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“For example, see the articles by Haff [16], Lin and Perlman [30], Dey and Srinivasan [12], Daniels and Kass [10], Ledoit and Wolf [26,27], Chen, Wiesel and Hero [9], Won et al.”
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“Ledoit and Wolf [47] provide guidance on a variety of approaches that have proven useful and Ueno and Nakamura [76] discussed the effect of several of those choices for regularization of CD on the data assimilation problem.”
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Self-citationOptimal Shrinkage-Based Portfolio Selection in High Dimensions
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“A straightforward way to improve the properties of the estimators for µn and Σn is to use the shrinkage approach (see, Jorion (1986), Ledoit and Wolf (2004)).”
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“The rotation I + Gss was addressed in random matrix theory [48] and covariance shrinkage [31] and is strong for close signal eigenvalues.”
BackgroundMethodInfluentialSparse portfolio selection via the sorted ℓ1-Norm
Kremer, P. J., Lee, S., Bogdan, M., & Paterlini, S. (2019) · Journal of Banking & Finance · doi:10.1016/j.jbankfin.2019.105687 · Cited by 63
Metabolic connectivity for differential diagnosis of dementing disorders
Titov, D., Diehl‐Schmid, J., Shi, K., Perneczky, R., Zou, N., Grimmer, T., Li, J., Drzezga, A. E., & Yakushev, I. Y. (2015) · Journal of Cerebral Blood Flow & Metabolism · doi:10.1177/0271678x15622465 · Cited by 63
“Otherwise, the estimation method is ill-posed, carrying a large estimation error.(23) Therefore, a sparse estimation of is preferable.”
MethodRibeiro, P. C., Audigier, R., & Pham, Q. C. (2015) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2015.11.001 · Cited by 63
Pantaleo, E., Tumminello, M., Mantegna, R. N., & Lillo, F. (2011) · Scuola Normale Superiore di Pisa · doi:10.1080/14697688.2010.534813 · Cited by 63
A Multifactor Perspective on Volatility‐Managed Portfolios
DeMiguel, V., Martín-Utrera, A., & Uppal, R. (2024) · The Journal of Finance · doi:10.1111/jofi.13395 · Cited by 62
Optimal Shrinkage Estimation of Variances With Applications to Microarray Data Analysis
Tong, T., & Wang, Y. (2007) · Journal of the American Statistical Association · doi:10.1198/016214506000001266 · Cited by 62
Direct shrinkage estimation of large dimensional precision matrix
Bodnar, T., Gupta, A. K., & Parolya, N. (2015) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2015.09.010 · Cited by 62
Tao, M., Wang, Y., & Zhou, H. H. (2013) · The Annals of Statistics · doi:10.1214/13-aos1128 · Cited by 62
Regularized Parameter Estimation in High-Dimensional Gaussian Mixture Models
Ruan, L., Yuan, M., & Zou, H. (2011) · Neural Computation · doi:10.1162/neco_a_00128 · Cited by 61
Cè, M., Gérardin, A., von Hippel, G. M., Meyer, H. B., Miura, K., Ottnad, K., Risch, A., José, T. S., Wilhelm, J., & Wittig, H. (2022) · Journal of High Energy Physics · doi:10.1007/jhep08(2022)220 · Cited by 61
“Still, we find relatively poor fit quality unless we use a shrunk estimator of the covariance matrix by scaling the off-diagonal elements of Cl according to [113, 114]”
MethodThe generalized shrinkage estimator for the analysis of functional connectivity of brain signals
Fiecas, M. J. A., & Ombao, H. (2011) · The Annals of Applied Statistics · doi:10.1214/10-aoas396 · Cited by 59
Metadata
- 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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