Other covariance estimators

[tlienart]

Cleaned up list

Shrinkage estimators

Linear Shrinkage

• [x] Ledoit Wolf, 2004, generic LW estimators
• [x] Schafer and Strimmer, 2005, generic LW estimators + modification with standardised matrices, see also corpcor package
• [ ] Opgen-Rhein & Strimmer 2007 shrinkage of variance
• [x] Chen et al 2010, OAS, RBLW estimators
• [ ] Touloumis 2014, a kind of OAS estimator? associated R package under GPL

Nonlinear Shrinkage

• [x] Ledoit Wolf, 2018

M-Estimators

• [ ] Maronna 1976 robust m-estimator
• [ ] Soloveychik, Wiesel 2014 COCA estimator based on Tyler's
• [ ] Tyler 1987 distribution free M-estimator of scatter

MCD estimators and related alternatives

• [ ] Rousseeuw, van Driessen 1999 Fast MCD, R package and also these considerations, also bear in mind that these estimators are not consistent as per Olive 2012
• [ ] Hubert, Rousseeuw, Verdonck 2011 Det MCD R package mirror and R package orig also maybe these slides
• [ ] Olive 2003 Median Ball Algorithm
• [ ] Devlin, Gnanadesikan, Kettenring 1975 DGK estimator
• [ ] Maronna, Zamar, 2002 Orthogonalised Gnanadesikan-Kettenring (OGK) estimator
• [ ] Olive 2009 RMVN estimator
• [ ] Zhang, Olive, Ye 2012 FCH, RFCH and RMVN

Thresholding estimators

HAC estimators

Rough list

(some of these may overlap)

• CHQBC (looks irrelevant)
• Tong and Wang probably similar to Strimmer's (looks irrelevant)

Other estimators

• the estimators in the covrob r package (Stahel-Donoho and related)
• HAC covariance estimation by Andrews implemented in CovarianceMatrices.jl and maybe consider the fast algorithm version by Heberle and Sattarhoff. Also related estimators like HC, QS-PW etc. see here
• nonlinear shrinkage estimation also Ledoit, Wolf
• POET by Fan Liao and Mincheva, see also review by Samworth and co: http://www.statslab.cam.ac.uk/~rjs57/YuSamworthDisc.pdf; it's on CRAN released under GPL2
• (??) Singular value thresholding by Cai, Candes and Shen
• LOREC by Luo others?

More links:

• http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.4595&rep=rep1&type=pdf
• https://arxiv.org/pdf/1504.02995.pdf
• https://www.mathworks.com/help/stats/robustcov.html

Repos

• (mit) https://github.com/karthikupadhya/covarianceEstimation-massiveMIMO
• (gpl2) fin cov reg https://github.com/yanyachen/FinCovRegularization
• graphical lasso for precision https://github.com/CamDavidsonPilon/Graphical-Lasso-in-Finance
• being robust in high dim can be practical (ICML17) - https://github.com/hoonose/robust-filter
• agnostic mean and cov https://github.com/kal2000/AgnosticMeanAndCovarianceCode
• robust high dim cov https://github.com/jwgoes/robust-highdim-covariance
• implementation of LW01 and LW17 https://github.com/RefaelLasry/EstimationOfCovarianceMatrix

[mateuszbaran]

Nice list, I would add one more:

• [ ] Nonlinear shrinkage estimation

[tlienart]

Ha cool, I saw that these guys published 3 or 4 papers but wasn't sure whether it was always about the same estimator or different ones. Will check.