The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
A well-conditioned estimator for large-dimensional covariance matrices
Open accessOverview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Markowitz, H. M. (1952) · The Journal of Finance · doi:10.1111/j.1540-6261.1952.tb01525.x · Cited by 18,429
Large Sample Properties of Generalized Method of Moments Estimators
Hansen, L. P. (1982) · Econometrica · doi:10.2307/1912775 · Cited by 13,467
Estimation with Quadratic Loss
James, W., & Stein, C. M. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_30 · Cited by 2,319
DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
Marčenko, V. A., & Pastur, L. A. (1967) · Mathematics of the USSR-Sbornik · doi:10.1070/sm1967v001n04abeh001994 · Cited by 1,713
Ledoit, O., & Wolf, M. (2003) · Journal of Empirical Finance · doi:10.1016/s0927-5398(03)00007-0 · Cited by 1,637
Self-citationThe Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?
Michaud, R. O. (1989) · Financial Analysts Journal · doi:10.2469/faj.v45.n1.31 · Cited by 1,384
Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices
Silverstein, J. W. (1995) · Journal of Multivariate Analysis · doi:10.1006/jmva.1995.1083 · Cited by 560
Estimation for Markowitz Efficient Portfolios
Jobson, J. D., & Korkie, B. (1980) · Journal of the American Statistical Association · doi:10.1080/01621459.1980.10477507 · Cited by 555
Limit of the Smallest Eigenvalue of a Large Dimensional Sample Covariance Matrix
Bai, Z., & Yin, Y. (1993) · The Annals of Probability · doi:10.1214/aop/1176989118 · Cited by 546
An Empirical Bayes Approach to Efficient Portfolio Selection
Frost, P. A., & Savarino, J. E. (1986) · Journal of Financial and Quantitative Analysis · doi:10.2307/2331043 · Cited by 391
Research works printed but not linked: 3
- S.A. Aivazyan, I.S. Yenukov, L.D. Meshalkin, Applied Statistics, Reference Edition M., Finances and Statistics, 1985 (Russian).
- Girko, 1986, G-analysis of observations of enormous dimensionality, Calculative Appl. Math., 60, 115
- Girko, 1986, G2-estimations of spectral functions of covariance matrices, Theor. Probab. Math. Statist., 35, 28
Cited by
Sorted by citations
Items 501–600 of 1,003
Sonali, P., & Kumar, D. N. (2020) · Journal of Water and Climate Change · doi:10.2166/wcc.2020.091 · Cited by 35
Robust and high-order correlation alignment for unsupervised domain adaptation
Cheng, Z., Chen, C., Chen, Z., Fang, K., & Jin, X. (2021) · Neural Computing and Applications · doi:10.1007/s00521-020-05465-7 · Cited by 35
Speer, S. P. H., Smidts, A., & Boksem, M. A. S. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.118761 · Cited by 34
Brownlees, C. T., Nualart, E., & Sun, Y. (2018) · Journal of Applied Econometrics · doi:10.1002/jae.2642 · Cited by 33
B → D * ℓ ν ℓ semileptonic form factors from lattice QCD with Möbius domain-wall quarks
Aoki, Y., Colquhoun, B., Fukaya, H., Hashimoto, S., Kaneko, T., Kellermann, R., KOPONEN, J. M., & Emi Kou, B. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.074503 · Cited by 33
Wang, P., Wang, Z., Li, H., & Himed, B. (2014) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2014.2338838 · Cited by 33
Shrinkage estimation in the frequency domain of multivariate time series
Böhm, H., & von Sachs, R. (2008) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2008.09.009 · Cited by 33
Enhanced Covariance Matrix Estimators in Adaptive Beamforming
Abrahamsson, R., Selén, Y., & Stoica, P. (2007) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2007.366399 · Cited by 33
Partial correlation financial networks
Millington, T., & Niranjan, M. (2020) · Applied Network Science · doi:10.1007/s41109-020-0251-z · Cited by 33
“To solve these issues we use the Ledoit-Wolf Covariance shrinkage method (Ledoit and Wolf 2004).”
MethodBodnar, T., & Okhrin, Y. (2011) · Scandinavian Journal of Statistics · doi:10.1111/j.1467-9469.2011.00729.x · Cited by 33
Supply, Demand and Monetary Policy Shocks in a Multi-Country New Keynesian ModelPreprint
Dées, S., Pesaran, M. H., Smith, L. V., & Smith, R. P. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1624798 · Cited by 33
Beyond Econometrics: A Roadmap Towards Financial Machine LearningPreprint
de Prado, M. L. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3365282 · Cited by 33
Yoo, K., Kim, J., Jang, J., & Kwak, N. (2022) · Findings of the Association for Computational Linguistics: ACL 2022 · doi:10.18653/v1/2022.findings-acl.289 · Cited by 33
Source enumeration for large array using shrinkage-based detectors with small samples
Huang, L., Qian, C., So, H. C., & Fang, J. (2015) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2014.130579 · Cited by 32
Penalized Covariance Matrix Estimation Using a Matrix-Logarithm Transformation
Deng, X., & Tsui, K. (2012) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2012.715556 · Cited by 32
Dwyer, R. S., Ricci, D. P., Colwell, L. J., Silhavy, T. J., & Wingreen, N. S. (2013) · Genetics · doi:10.1534/genetics.113.155861 · Cited by 32
Adegoke, N. A., Smith, A. N. H., Anderson, M. J., Abbasi, S. A., & Pawley, M. D. M. (2018) · Computers & Industrial Engineering · doi:10.1016/j.cie.2018.02.008 · Cited by 32
Shin, J., Kim, D.-W., Müller, K., & Hwang, H.-J. (2018) · Sensors · doi:10.3390/s18061827 · Cited by 32
Frontoparietal action-oriented codes support novel instruction implementation
González‐García, C., Formica, S., Wisniewski, D., & Braß, M. (2020) · NeuroImage · doi:10.1016/j.neuroimage.2020.117608 · Cited by 32
Theory and Practice of GVAR Modeling
Dallas, F. R. B. O., Chudík, A., & Pesaran, M. H. (2014) · Federal Reserve Bank of Dallas, Globalization and Monetary Policy Institute Working Papers · doi:10.24149/gwp180 · Cited by 32
Guo, X., Tinaz, S., & Dvornek, N. C. (2022) · Frontiers in Neuroimaging · doi:10.3389/fnimg.2022.952084 · Cited by 34
“The FC matrices were calculated using the Ledoit Wolf estimator (Ledoit and Wolf, 2004) for large covariance matrices, and only the upper triangle of the matrices were used as the inputs of the ML classifiers to prevent redundancy since the FC matrices are symmetric.”
MethodToward FRP-Based Brain-Machine Interfaces—Single-Trial Classification of Fixation-Related Potentials
Finke, A., Essig, K., Marchioro, G., & Ritter, H. J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0146848 · Cited by 32
Regularized continuous estimation of distribution algorithms
Karshenas, H., Santana, R., Bielza, C., & Larrañaga, P. (2012) · Applied Soft Computing · doi:10.1016/j.asoc.2012.11.049 · Cited by 32
Better Estimates of Genetic Covariance Matrices by “Bending” Using Penalized Maximum Likelihood
Meyer, K., & Kirkpatrick, M. (2010) · Genetics · doi:10.1534/genetics.109.113381 · Cited by 32
Constructing Multi‐Country Rational Expectations Models
Dées, S., Pesaran, M. H., Smith, L. V., & Smith, R. P. (2013) · Oxford Bulletin of Economics and Statistics · doi:10.1111/obes.12046 · Cited by 32
Wittevrongel, B., & Hulle, M. M. V. (2017) · Frontiers in Neuroscience · doi:10.3389/fnins.2017.00630 · Cited by 32
“However, several methods for covariance matrix estimation with a small number of samples have been described (e.g., shrinkage, Ledoit and Wolf, 2004, regularization, Friedman, 1989, among others) and can be assessed in terms of improving the estimation of the covariance matrix.”
MethodRegularized Mixture Density Estimation With an Analytical Setting of Shrinkage Intensities
Halbe, Z., Bortman, M., & Aladjem, M. E. (2013) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2012.2234477 · Cited by 31
Interpolation-Based Inference of Vessel Trajectory Waypoints from Sparse AIS Data in Maritime
Zaman, B., Marijan, D., & Kholodna, T. (2023) · Journal of Marine Science and Engineering · doi:10.3390/jmse11030615 · Cited by 31
“Different covariance estimators, i.e., shrunk covariance [44], Oracle Approximating Shrinkage (OAS) [44], minimum covariance determinant [45], elliptical envelope [46], and Ledoit-Wolf [47] estimators, have been tested to be used in hybrid RBW for covariance estimation.”
MethodA Flexible Estimating Equations Approach for Mapping Function-Valued Traits
Xiong, H., Goulding, E. H., Carlson, E. J., Tecott, L. H., McCulloch, C. E., & Sen, Ś. (2011) · Genetics · doi:10.1534/genetics.111.129221 · Cited by 32
Classification of Eye Fixation Related Potentials for Variable Stimulus Saliency
Wenzel, M. A., Golenia, J.-E., & Blankertz, B. (2016) · Frontiers in Neuroscience · doi:10.3389/fnins.2016.00023 · Cited by 31
Hübner, D., Verhoeven, T., Müller, K., Kindermans, P.-J., & Tangermann, M. (2018) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2018.2807039 · Cited by 31
“Hence, the authors of the latter study used only one classifier and applied the same linear classifier with covariance-shrinkage by Ledoit-Wolf [58], [71] to all three classifiers.”
MethodHybrid Processing Design for Multipair Massive MIMO Relaying With Channel Spatial Correlation
Fozooni, M., Ngo, H. Q., Matthaiou, M., Jin, S., & Alexandropoulos, G. C. (2018) · IEEE Transactions on Communications · doi:10.1109/tcomm.2018.2867490 · Cited by 31
Improving the condition number of estimated covariance matrices
Tabeart, J. M., Dance, S. L., Lawless, A. S., Nichols, N. K., & Waller, J. A. (2019) · Tellus A Dynamic Meteorology and Oceanography · doi:10.1080/16000870.2019.1696646 · Cited by 31
“…with sampling error, which manifest in sample covariance matrices, or other covariance matrix estimates, that are very ill-conditioned or can fail to satisfy required properties of covariance matrices (such as symmetry and positive semi-definiteness) [Higham et al., 2016, Ledoit and Wolf, 2004].”
BackgroundMethodA comprehensive appraisal of style-integration methods
Fernández-Pérez, A., Fuertes, A.-M., & Miffre, J. (2017) · Journal of Banking & Finance · doi:10.1016/j.jbankfin.2019.05.016 · Cited by 37
“We entertain other OI strategies where the style-weighting vector, ωωtt in Equation (1), is derived by maximizing: i) the mean-variance utility as in the main section of the paper but with covariance matrix estimator based on the shrinkage approach of Ledoit and Wolf (2004) to”
MethodSeismic data assimilation with an imperfect model
Alfonzo, M., & Oliver, D. S. (2019) · Computational Geosciences · doi:10.1007/s10596-019-09849-0 · Cited by 31
“We have chosen to shrink the low-rank sample covariance estimate towards the diagonal matrix whose diagonal elements are all equal to the average of the diagonal elements of the sample covariance matrix [34, 53].”
MethodAgurto, C., Cecchi, G., Norel, R., Ostrand, R., Kirkpatrick, M. G., Baggott, M. J., Wardle, M. C., de Wit, H., & Bedi, G. (2020) · Neuropsychopharmacology · doi:10.1038/s41386-020-0620-4 · Cited by 31
“More speci fi cally, partial correlations were calculated using the inverse of the regularized covariance matrix [34].”
MethodRegularized Tapered Sample Covariance Matrix
Ollila, E., & Breloy, A. (2022) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2022.3169269 · Cited by 33
“The estimators included in the study are: i ) The Ledoit-Wolf estimator ( LWE ) [2] defined by (1) where β is an estimate of an (oracle) MMSE parameter β o . ii ) The shrinkage to tapering oracle approximate ( STOA ) estimator [14] defined by (6) where β is an estimate of the oracle parameter…”
BackgroundMethodThe genetic architecture of language functional connectivity
Mekki, Y., Guillemot, V., Lemaître, H., Carrión-Castillo, A., Forkel, S. J., Frouin, V., & Philippe, C. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.118795 · Cited by 31
Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities
Pesaran, M. H., & Yamagata, T. (2023) · Journal of Financial Econometrics · doi:10.1093/jjfinec/nbad002 · Cited by 31
Diversified minimum-variance portfolios
Coqueret, G. (2014) · Annals of Finance · doi:10.1007/s10436-014-0253-x
An Efficient P300-based Brain-Computer Interface with Minimal Calibration Time
Lotte, F., & Guan, C. (2009) · HAL · Cited by 31
Nearest neighbor conditional estimation for Harris recurrent Markov chains
Sancetta, A. (2009) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2009.06.013 · Cited by 31
D -meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
Bazavov, A., DeTar, C. E., El-Khadra, A. X., Gamiz, E., Gelzer, Z. J., Gottlieb, S., Jay, W. I., Jeong, H., Kronfeld, A. S., Li, R., et al. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.094516 · Cited by 30
On the Combination of Naive and Mean-Variance Portfolio Strategies
Lassance, N., Vanderveken, R., & Vrins, F. D. (2023) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2023.2256801 · Cited by 30
Couillet, R., Kammoun, A., & Pascal, F. (2015) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2015.08.021 · Cited by 30
On Preserving Original Variables in Bayesian PCA With Application to Image Analysis
Li, J., & Tao, D. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2211372 · Cited by 29
On the Performance of MUSIC With Toeplitz Rectification in the Context of Large Arrays
Vallet, P., & Loubaton, P. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2017.2742988 · Cited by 30
“[14]–[17]) and requires restrictive assumptions such as the vanishing of the off-diagonal entries of R at a sufficiently fast rate, as M → ∞.”
BackgroundOn the covariance matrix of the stationary distribution of a noisy dynamical system
Oku, M., & Aihara, K. (2018) · Nonlinear Theory and Its Applications IEICE · doi:10.1587/nolta.9.166 · Cited by 30
Estimating Phylogenies from Shape and Similar Multidimensional Data: Why It Is Not Reliable
Varón‐González, C., Whelan, S., & Klingenberg, C. P. (2020) · Systematic Biology · doi:10.1093/sysbio/syaa003 · Cited by 30
Riemannian Geometry-Based Decoding of the Directional Focus of Auditory Attention Using EEG
Geirnaert, S., Francart, T., & Bertrand, A. (2021) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp39728.2021.9413404 · Cited by 30
“As in [2], we estimate the covariance matrices using ridge regression, where the regularization hyperparameter is determined automatically using the method proposed in [10].”
MethodBagheri, M., & Power, S. (2022) · Sensors · doi:10.3390/s22020535 · Cited by 30
“A regularized LDA algorithm was used for classification [37].”
MethodYousedian, A., Shayegh, F., & Maleki, Z. (2023) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2022.904770 · Cited by 35
Ebtehaj, A. M., & Foufoula‐Georgiou, E. (2013) · Water Resources Research · doi:10.1002/wrcr.20424 · Cited by 30
A Probabilistic Framework to Infer Brain Functional Connectivity from Anatomical Connections
Deligianni, F., Varoquaux, G. P., Thirion, B., Robinson, E. C., Sharp, D. J., Edwards, A. D., & Rueckert, D. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-22092-0_25 · Cited by 29
Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework
Hannart, A., & Naveau, P. (2014) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2014.06.001 · Cited by 30
Pamukçu, E., Bozdogan, H., & Çalık, S. (2015) · Computational and Mathematical Methods in Medicine · doi:10.1155/2015/370640 · Cited by 30
Using industry momentum to improve portfolio performance
Behr, P., Guettler, A., & Trübenbach, F. (2011) · Journal of Banking & Finance · doi:10.1016/j.jbankfin.2011.12.007 · Cited by 30
Kalantzis, V., Bekas, C., Curioni, A., & Gallopoulos, E. (2013) · Numerical Algorithms · doi:10.1007/s11075-012-9687-2 · Cited by 30
Varoquaux, G. P., Gramfort, A., Poline, J.-B., & Thirion, B. (2012) · Journal of Physiology-Paris · doi:10.1016/j.jphysparis.2012.01.001 · Cited by 32
Estimating the functional dimensionality of neural representations
Ahlheim, C., & Love, B. C. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2018.06.015 · Cited by 30
“We used the residual time-series from the fitted GLM to estimate the noise covariance Σnoise and used regularization to shrink it towards the diagonal (Ledoit and Wolf, 2004).”
MethodSanam, T. F., & Godrich, H. (2020) · IEEE Access · doi:10.1109/access.2020.2982277 · Cited by 30
Shrinkage Approach for Spatiotemporal EEG Covariance Matrix Estimation
Beltrachini, L., von Ellenrieder, N., & Muravchik, C. H. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2238532 · Cited by 29
Use of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation
Kuismin, M., & Sillanpää, M. J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0148171 · Cited by 29
Structure Tensor Riemannian Statistical Models for CBIR and Classification of Remote Sensing Images
Rosu, R.-G., Donias, M., Bombrun, L., Said, S., Regniers, O., & da Costa, J. (2016) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2016.2604680 · Cited by 29
A Regularized GLS for Structural Equation Modeling
Arruda, E. H., & Bentler, P. M. (2017) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2017.1318392 · Cited by 29
“Inverting such an ill-conditioned matrix amplifies estimation error dramatically (Ledoit & Wolf, 2004), in turn leading to unstable estimates.”
BackgroundMethodOptimal and robust combination of forecasts via constrained optimization and shrinkage
Roccazzella, F., Gambetti, P., & Vrins, F. D. (2021) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2021.04.002 · Cited by 29
On Accurate Source Enumeration: A New Bayesian Information Criterion
Ke, X., Zhao, Y. C., & Huang, L. (2021) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2021.3052052 · Cited by 29
Portfolio selection with parsimonious higher comoments estimation
Lassance, N., & Vrins, F. D. (2021) · Journal of Banking & Finance · doi:10.1016/j.jbankfin.2021.106115 · Cited by 29
Identification and prediction of urban airspace availability for emerging air mobility operations
Murça, M. C. R. (2021) · Transportation Research Part C Emerging Technologies · doi:10.1016/j.trc.2021.103274 · Cited by 29
Covariance Matrix Estimation for FDA-MIMO Adaptive Transmit Power Allocation
Wang, L., Wang, W.-Q., & So, H. C. (2022) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2022.3184780 · Cited by 29
The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors?
Nguyen, A. P. N., Mai, T. T., Bezbradica, M., & Crane, M. (2022) · Entropy · doi:10.3390/e24091317 · Cited by 29
“, the noise is removed completely without the loss of data information [77,78].”
BackgroundCalibration-Free BCI Based Control
Grizou, J., Iturrate, I., Montesano, L., Oudeyer, P., & Lopes, M. C. (2014) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v28i1.8923 · Cited by 29
Robust adaptive acoustic vector sensor beamforming using automated diagonal loading
Zhang, Y., Sun, D., & Zhang, D. (2009) · Applied Acoustics · doi:10.1016/j.apacoust.2009.03.004 · Cited by 29
A Framework for Inter-Subject Prediction of Functional Connectivity From Structural Networks
Deligianni, F., Varoquaux, G. P., Thirion, B., Sharp, D. J., Ledig, C., Leech, R., & Rueckert, D. (2013) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2013.2276916 · Cited by 28
Tracking and outperforming large stock-market indices
Gnägi, M., & Strub, O. (2018) · Omega · doi:10.1016/j.omega.2018.11.008 · Cited by 29
“We use the estimator of Ledoit and Wolf [20] to estimate the covariances σ ij based on the discrete in-sample returns of the assets i, j ∈ U ∪ { n + 1 .”
MethodInfluentialTesting CAPM with a Large Number of AssetsPreprint
Pesaran, M. H., & Yamagata, T. (2012) · SSRN Electronic Journal · doi:10.2139/ssrn.2020423 · Cited by 29
Inferring trade directions in fast markets
Jurkatis, S. (2021) · Journal of Financial Markets · doi:10.1016/j.finmar.2021.100635 · Cited by 28
Generative modeling and augmentation of EEG signals using improved diffusion probabilistic models
Torma, S., & Szegletes, L. (2024) · Journal of Neural Engineering · doi:10.1088/1741-2552/ada0e4 · Cited by 33
“Temporal connectivity maps were calculated using the Nilearn Python package [30] in which correlation maps were defined using the Ledoit–Wolf covariance estimator [31].”
Co-variance guided Artificial Bee Colony
Kumar, D., & Mishra, K. K. (2018) · Applied Soft Computing · doi:10.1016/j.asoc.2018.04.050 · Cited by 28
Accelerating Bayesian Synthetic Likelihood With the Graphical Lasso
An, Z., South, L. F., Nott, D. J., & Drovandi, C. (2018) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2018.1537928 · Cited by 28
“It is well known that the sample covariance matrix is unbiased but for small to moderate n it performs poorly as an estimator with respect to a variety of loss functions (see, e.g., Ledoit and Wolf 2004).”
BackgroundImproved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review
Sun, R., Ma, T., Liu, S., & Sathye, M. (2019) · Journal of risk and financial management · doi:10.3390/jrfm12010048 · Cited by 28
“Ledoit and Wolf (2003, 2004) used a linear combination of sample covariance matrices and a target matrix to estimate the covariance matrix, where the target matrix could be the identity matrix, or the covariance matrix estimated by the one factor model and applied this method to the portfolio…”
MethodAttribution of Detected Temperature Trends in Southeast Brazil
de Abreu, R. C., Tett, S. F. B., Schurer, A., & da Rocha, H. R. (2019) · Geophysical Research Letters · doi:10.1029/2019gl083003 · Cited by 28
“However, Ledoit and Wolf (2004) method showed indications of leading to a more powerful statistical test, with a lower mean squared error, and is more objective than truncating to the leading k eigenvectors, which depends on the choice of k (Ribes et al., 2009).”
MethodPowerful knockoffs via minimizing reconstructability
Spector, A., & Janson, L. (2022) · The Annals of Statistics · doi:10.1214/21-aos2104 · Cited by 28
“the same data used to run knockoffs, using one of three methods: Ledoit–Wolf estimation (Ledoit and Wolf, 2004), the graphical lasso algorithm (Friedman et al.”
MethodTriana-Guzman, N., Orjuela-Cañón, Á. D., Jutinico, A. L., Mendoza-Montoya, O., & Antelis, J. M. (2022) · Frontiers in Neuroinformatics · doi:10.3389/fninf.2022.961089 · Cited by 28
Covariance matrix repairing in Gaussian based EDAs
Dong, W., & Yao, X. (2007) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2007.4424501 · Cited by 28
Multimodel Shrinkage for Knowledge-Aided Space-Time Adaptive Processing
Riedl, M., & Potter, L. C. (2018) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2018.2813898 · Cited by 28
An adaptive CSP filter to investigate user independence in a 3-class MI-BCI paradigm
Costa, A. P., Møller, J. S., Iversen, H. K., & Puthusserypady, S. K. (2018) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2018.09.021 · Cited by 28
Eisenkolb, V. M., Held, L. M., Utzschmid, A., Lin, X., Krieg, S. M., Meyer, B., Gempt, J., & Jacob, S. N. (2023) · Cell Reports · doi:10.1016/j.celrep.2023.112467 · Cited by 30
Li, J., Guo, W., Wei, F., Zhang, T., & Yu, W. (2024) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2024.3441548 · Cited by 27
Integrated Optimal Fingerprinting: Method Description and Illustration
Hannart, A. (2015) · Journal of Climate · doi:10.1175/jcli-d-14-00124.1 · Cited by 26
Improving zero-training brain-computer interfaces by mixing model estimators
Verhoeven, T., Hübner, D., Tangermann, M., Müller, K. R., Dambre, J., & Kindermans, P.-J. (2017) · Journal of Neural Engineering · doi:10.1088/1741-2552/aa6639 · Cited by 27
“An optimal value for λ can be found with the Ledoit–Wolf formula [23, 25, 26].”
MethodA Distributionally Robust Minimum Variance Beamformer Design
Li, B., Rong, Y., Sun, J., & Teo, K. L. (2017) · IEEE Signal Processing Letters · doi:10.1109/lsp.2017.2773601 · Cited by 27
Zhao, N., Zhan, X., Guthrie, K. A., Mitchell, C. M., & Larson, J. C. (2018) · Genetic Epidemiology · doi:10.1002/gepi.22127 · Cited by 27
“They further developed methods to obtain the optimal 𝜆 when 𝑻 = 𝑫 (Ledoit & Wolf, 2004).”
MethodComparing high-dimensional conditional covariance matrices: Implications for portfolio selection
Moura, G. V., Santos, A. A. P., & Ruiz, E. (2020) · Journal of Banking & Finance · doi:10.1016/j.jbankfin.2020.105882 · Cited by 27
Neuroadaptive modelling for generating images matching perceptual categories
Kangassalo, L., Spapé, M., & Ruotsalo, T. (2020) · Scientific Reports · doi:10.1038/s41598-020-71287-1 · Cited by 27
Muting, not fragmentation, of functional brain networks under general anesthesia
Areshenkoff, C. N., Nashed, J. Y., Hutchison, R. M., Hutchison, M., Levy, R., Cook, D. J., Menon, R. S., Everling, S., & Gallivan, J. P. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.117830 · Cited by 27
Flasseur, O., Thé, S., Denis, L., Thiébaut, É., & Langlois, M. (2021) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202038957 · Cited by 27
Recent advances in shrinkage-based high-dimensional inference
Bodnar, O., Bodnar, T., & Parolya, N. (2021) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2021.104826 · Cited by 27
Lai, Z., & Yang, H. (2022) · ACM Computing Surveys · doi:10.1145/3485274 · Cited by 29
“Σ̂W E is a well-conditioned estimator for a large-dimensional covariance matrix [Ledoit and Wolf 2004] and μ̂ J S is a James-Stein estimator [Efron and Morris 1973; James and Stein 1961; Jorion 1986].”
BackgroundMethodHyperspectral Anomaly Detection: Comparative Evaluation in Scenes with Diverse Complexity
Borghys, D. C. J., Kåsen, I., Achard, V., & Perneel, C. (2012) · Journal of Electrical and Computer Engineering · doi:10.1155/2012/162106 · Cited by 27
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
