Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices

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High‐dimensional covariance matrix estimation (2019, methodology): “Warton (2008) proposed linear shrinkage to shrink the sample correlation matrix towards the identity, and proposed to use a K -fold cross-validation to estimate the shrinkage parameter.”
Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “Warton (2008) taking α2 = 1 showed that such ridge estimators can be obtained using the penalized normal likelihood where the penalty term is proportional to trΣ−1.”
RRPP: An r package for fitting linear models to high‐dimensional data using residual randomization (2018, methodology): “The manylm and anova.manylm functions can optionally use ridge regularization (Warton, 2008) for obtaining appropriately ranked covariance matrices in a penalized- likelihood framework.”
So Many Variables: Joint Modeling in Community Ecology. (2015, background): “Historically, the large number of taxa to be jointly analyzed, relative to the information available on each, has been technically challenging [8].”
Bayesian Synthetic Likelihood (2017, methodology): “…of the synthetic likelihood estimator, and to help ensure that MCMC mixes reasonably 2021) consider using the covariance shrinkage estimator of Warton (2008): where ¯ R M is the correlation matrix and ¯Σ d,M is the diagonal matrix of variances, all estimated using M model simulations for a…”