Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics

By Juliane Schäfer, Korbinian Strimmer. 2011

1,727 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

In Molecular Biology

Citations in the corpus

Nonparametric Independence Testing for Small Sample Sizes (2014, background): “Over the decades, there have been many estimators proposed for covariance matrices that outperform the sample covariance matrix in different situations - see [10, 11, 12, 13].”
Optimal Whitening and Decorrelation (2015, methodology): “…dimension d the standard unbiased empirical covariance S = ( s ij ) with s ij = In high-dimensional cases with p > n the empirical estimator breaks down, and the covariance matrix needs to be estimated by a suitable regularized method instead (e.g. Schäfer and Strimmer, 2005; Pourahmadi, 2011).”
ppcor: An R Package for a Fast Calculation to Semi-partial Correlation Coefficients (2015, methodology): “The R package corpcor (Schafer and Strimmer, 2005) provides the function cor2pcor() for computing partial correlation from correlation matrix and vice versa.”
The Feature Importance Ranking Measure (2009, background): “However, it is possible to estimate it reliably even from high-dimensional data using mean-squared-error optimal shrinkage [7].”
Adaptive Stochastic Gradient Descent Optimisation for Image Registration (2009, positive): “would require a larger N . An interesting technique that combines the two approaches is the shrinkage method described in Schafer and Strimmer (2005) .”
High‐dimensional covariance matrix estimation (2019, background): “This falls into the so-called rotation-equivariant class of estimators used in Stein (1975). The simplicity of Σ̂LS attracted a lot of similar studies.”
The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation (2020, methodology): “The target (2.5) was first suggested by (Ledoit, 1995, Appendix B.1), then was also proposed by Schäfer and Strimmer (2005) in a different context related to genomics, and has been used by Wolf and Wunderli (2012) to estimate the covariance matrix of a universe of hedge fund returns.”
Inferring cellular networks – a review (2007, neutral): “In one study, Schäfer and Strimmer [21] use bootstrap resampling together with the Moore-Penrose pseudoinverse and false discovery rate multiple testing, while in another [23], they discuss a linear shrinkage approach to regularization.”
Partial Correlation Estimation by Joint Sparse Regression Models (2008, methodology): “shrinkage covariance estimation procedure to overcome the ill-conditioned problem of sample covariance matrix when p > n (Schafer and Strimmer 2007); and a hard thresholding method to regularize the covariance matrix for families of covariance matrices satisfying suitable sparsity assumptions (Bicke”
Sequential Covariance-Matrix Estimation with Application to Mitigating Catastrophic Forgetting (2015, methodology): “We briefly review single-target shrinkage estimator by following [13], [17], which is generally applied to highdimensional estimation problems.”