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A well-conditioned estimator for large-dimensional covariance matrices
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“Moreover, since rank deficiency is often a problem for matrix inversion, we additionally tested a shrinkage transformation (Ledoit and Wolf, 2004) for the covariance matrix.”
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“…straightforward, Equation 2 indicates that estimating partial correlations requires inverting the sample covariance matrix Σ. Typically, Σ is estimated via maximum likelihood (ML) but this approach yields reliable estimates only under ideal conditions (Ledoit & Wolf, 2004b; Won, Lim, & Kim, 2009).”
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“dimension using shrinkage regularized linear discriminant analysis (LDA (34)).”
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“However, since these are M × M matrices (i.e., relatively large matrices), we might need to regularize the estimates [8], [9].”
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“We identify the optimal shrinkage parameter analytically, as was shown in (Blankertz et al., 2011; Ledoit and Wolf, 2004).”
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“…roustly from limited numbers of samples, several enhanced estimaion methods exist, e.g., probabilistic principal component analysis Tipping and Bishop, 1999 ), minimum covariance determinant esti- ation ( Rousseeuw and Driessen, 1999 ) or the Ledoit-Wolf shrinkage odel ( Ledoit and Wolf, 2004a ).”
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“Thus, assuming homogeneity, in [9] the Maximum Likelihood (ML) covariance matrix estimator is derived modeling the disturbance as the sum of a coloured interference plus white disturbance; in [10], the ML estimation of an unstructured covariance matrix with a condition number upper bound requirement is considered; in…”
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“To exemplify this, we performed a typical classification approach, discriminating between resting vs. stimulation trials in a 10-fold cross validation using regularized Linear Discriminant Analysis with automatic shrinkage of the covariance matrices (Ledoit and Wolf, 2004; Blankertz et al., 2011).”
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“To cope with the dimensionality challenge, particularly when the number of observations is smaller than the number of time series, typical solutions involve factor models [4], [5], shrinkage estimators [6], [7], and low-rank data representations [3].”
BackgroundMethodFine-grain atlases of functional modes for fMRI analysis
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Adaptive covariance matrix estimation through block thresholding
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“Ledoit and Wolf (2004, 2017) recommend the use of shrinkage covariance matrix estimators in place of the sample covariance matrix.”
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“Because the number of prototypes is usually small compared to the dimension of the covariance matrix, we use the LedoitWolf method [22] to obtain a more robust estimation of Σ.”
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“According to [32]–[34], when the maximum Doppler frequency fd in the CoDSC is large, the value of Cond (HTD) fluctuates significantly and mostly concentrates in a large numerical interval.”
BackgroundUnified Framework to Regularized Covariance Estimation in Scaled Gaussian Models
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Robust Estimation of Structured Covariance Matrix for Heavy-Tailed Elliptical Distributions
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Financial Risk Measurement for Financial Risk Management
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“Similar to the approach of [108], the same starting point was taken by [122], where the well-known Ledoit–Wolf estimator has been introduced.”
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Self-citationRotational Invariant Estimator for General Noisy Matrices
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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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