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A well-conditioned estimator for large-dimensional covariance matrices
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“Ledoit and Wolf (2004) considered a Steinian estimate that shrinks the sample covariancematrix towards the identity matrix.”
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“…j r � ̂ ,ii � ̂ ,jj, i≠ j , | 693PROIETTI and GIOVannELLI The parameter λ is estimated by minimizing the mean square nowcast error, for example performing a grid search over the unit interval or applying the closed form estimator by Ledoit and Wolf (2004a), reported in Section 4 of the Supplement.”
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“8) which is asymptotically unbiased [55] but has a highvariance, one can employ a shrinkage estimator [84, 85] which reduces the overall estimator error by trading larger bias for lower variance.”
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“This is a desirable penalization following the results of Ledoit and Wolf (2004b) but the ensuing penalized log-likelihood has to be minimized using the iterative quadratic programming algorithm, which could possibly be slow.”
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“Alternatively, one can use an analytical estimate following the arguments of Ledoit & Wolf [20].”
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“Following Engle et al. (2019), we obtained the covariance matrix by applying alternatively the linear shrinkage approach proposed in Ledoit & Wolf (2004) and the non-linear shrinkage approach based on Ledoit & Wolf (2012), Ledoit & Wolf (2015) and Ledoit & Wolf (2016).”
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“Indeed, Ledoit-Wolf [26] developed a method for estimating the optimal ridge in a least squares error case, which has been used in BCI research [16], [20], [23].”
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“The shrinkage parameter was calculated with an analytic method [38, 39].”
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“(4) This loss function is maximized by ̂(ν) = [(1−ν)S+νT−1]−1 with ν = λ(1 + λ)−1 ∈ (0, 1), which coincides with the inverse of the shrunken covariance estimator of Ledoit and Wolf (2004).”
BackgroundMethodInfluentialTesting and estimating change-points in the covariance matrix of a high-dimensional time series
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“Instead, they are estimated from limited and noisy training data, which makes the parameter values (19)”
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“This is in line with past findings of a tight relationship between working memory and attention (Awh et al., 2006; Awh & Jonides, 2001; Chun, 2011).”
A metric space for Type Ia supernova spectra
Sasdelli, M., Hillebrandt, W., Aldering, G., Antilogus, P. E., Aragon, C., Bailey, S., Baltay, C., Benitez-Herrera, S., Bongard, S., Buton, C., et al. (2014) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stu2416 · Cited by 21
Higashi, H., Rutkowski, T. M., Tanaka, T., & Tanaka, Y. (2016) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2016.2599297 · Cited by 21
Risk-Based Portfolios with Large Dynamic Covariance Matrices
Nakagawa, K., Imamura, M., & Yoshida, K. (2018) · International Journal of Financial Studies · doi:10.3390/ijfs6020052 · Cited by 21
“In order to reduce the estimation error, the linear shrinkage method of Ledoit and Wolf (2004) is often used.”
MethodDesigning Phase-Sensitive Common Spatial Pattern Filter to Improve Brain-Computer Interfacing
Chakraborty, B., Ghosh, L., & Konar, A. (2019) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2019.2954470 · Cited by 21
“Table-V includes the classifier accuracy obtained by the proposed AP-CSP algorithm against the existing CSP algorithms: Composite CSP (CCSP) [32], Regularized CSP with Generic Learning (GLRCSP) [33], Spatially Regularized CSP (SRCSP) [6], CSP with regularized covariance matrices determined by Ledoit and Wolf’s method…”
MethodRobust multivariate control chart based on shrinkage for individual observations
Cabana, E., & Lillo, R. E. (2021) · Journal of Quality Technology · doi:10.1080/00224065.2021.1930617 · Cited by 21
“On the other hand, as stated in Ledoit and Wolf (2004), when the dimension p is larger than the number n of observations available, the sample covariance matrix is not even invertible.”
BackgroundMethodHybrid fNIRS-EEG based discrimination of 5 levels of memory load
Herff, C., Fortmann, O., Tse, C., Cheng, X., Putze, F., Heger, D., & Schultz, T. (2015) · International IEEE/EMBS Conference on Neural Engineering · doi:10.1109/ner.2015.7146546 · Cited by 20
A note on improving quadratic inference functions using a linear shrinkage approach
Han, P., & Song, P. X. ‐. (2010) · Statistics & Probability Letters · doi:10.1016/j.spl.2010.12.010 · Cited by 21
A method for outdoor skateboarding video games
Anlauff, J., Weitnauer, E., Lehnhardt, A., Schirmer, S., Zehe, S., & Tonekaboni, K. (2010) · International Conference on Advances in Computer Entertainment Technology (ACE) · doi:10.1145/1971630.1971642 · Cited by 21
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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