Schäfer Strimmer covariance shrinkage

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).

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;

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.

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
true_cov <- matrix(c(3, 2, 2, 2), nrow = 2)
chol_true_cov <- chol(true_cov)
true_mean <- c(0, 0)

# Generate samples
set.seed(42)
x <- replicate(nSamples, true_mean) +
  t(chol_true_cov) %*% matrix(stats::rnorm(pTrue * nSamples),
    nrow = pTrue, ncol = nSamples
  )
x <- t(x)
res_shrinkage <- schaferStrimmer_cov(x)
res_shrinkage$lambda_star # should be 0.01287923
#> [1] 0.01287923