schaferStrimmer_cov {bayesRecon}

Schäfer Strimmer covariance shrinkage

Description

Computes the Schäfer Strimmer shrinkage estimator for a covariance matrix from a matrix of samples.

Usage

schaferStrimmer_cov(x)

Arguments

x

matrix of samples with dimensions nxp (n samples, p dimensions).

Details

This function computes the shrinkage to a diagonal covariance with unequal variances. Note that here we use the estimators S = X X^T/n and T = diag(S) and we internally use the correlation matrix in place of the covariance to compute the optimal shrinkage factor.

Value

A list containing the shrinkage estimator and the optimal lambda. The list has the following named elements:

• shrink_cov: the shrinked covariance matrix (p x p);

• lambda_star: the optimal lambda for the shrinkage;

References

Schäfer, Juliane, and Korbinian Strimmer. (2005). A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics. Statistical Applications in Genetics and Molecular Biology 4: Article32. doi:10.2202/1544-6115.1175.

Examples

# Generate some multivariate normal samples
# Parameters
nSamples <- 200
pTrue <- 2

# True moments
trueSigma <- matrix(c(3,2,2,2), nrow=2)
chol_trueSigma <- chol(trueSigma)
trueMean <- c(0,0) 

# Generate samples
set.seed(42)
x <- replicate(nSamples, trueMean) +  t(chol_trueSigma)%*%matrix(rnorm(pTrue*nSamples), 
                                                                 nrow=pTrue,ncol=nSamples)
x <- t(x) 
res_shrinkage <- schaferStrimmer_cov(x)
res_shrinkage$lambda_star # should be 0.01287923