shrink.intensity: Estimation of Shrinkage Intensities

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

The functions estimate.lambda and estimate.lambda.var shrinkage intensities used for correlations and variances used in cor.shrink and var.shrink, respectively.

Usage

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estimate.lambda(x, w, verbose=TRUE)
estimate.lambda.var(x, w, verbose=TRUE)

Arguments

x

a data matrix

w

optional: weights for each data point - if not specified uniform weights are assumed (w = rep(1/n, n) with n = nrow(x)).

verbose

report shrinkage intensities (default: TRUE)

Details

var.shrink computes the empirical variance of each considered random variable, and shrinks them towards their median. The corresponding shrinkage intensity lambda.var is estimated using

λ_{var}^{*} = ( ∑_{k=1}^p Var(s_{kk}) )/ ∑_{k=1}^p (s_{kk} - median(s))^2

where median(s) denotes the median of the empirical variances (see Opgen-Rhein and Strimmer 2007).

Similarly, cor.shrink computes a shrinkage estimate of the correlation matrix by shrinking the empirical correlations towards the identity matrix. In this case the shrinkage intensity lambda equals

λ^{*} = ∑_{k \neq l} Var(r_{kl}) / ∑_{k \neq l} r_{kl}^2

(Sch\"afer and Strimmer 2005).

Ahdesm\"aki suggested (2012) a computationally highly efficient algorithm to compute the shrinkage intensity estimate for the correlation matrix (see the R code for the implementation).

Value

estimate.lambda and estimate.lambda.var returns a number between 0 and 1.

Author(s)

Juliane Sch\"afer, Rainer Opgen-Rhein, Miika Ahdesm\"aki and Korbinian Strimmer (http://strimmerlab.org).

References

Opgen-Rhein, R., and K. Strimmer. 2007. Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach. Statist. Appl. Genet. Mol. Biol. 6:9. <DOI:10.2202/1544-6115.1252>

Sch\"afer, J., and K. Strimmer. 2005. A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol. 4:32. <DOI:10.2202/1544-6115.1175>

See Also

cor.shrink, var.shrink.

Examples

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# load corpcor library
library("corpcor")

# small n, large p
p = 100
n = 20

# generate random pxp covariance matrix
sigma = matrix(rnorm(p*p),ncol=p)
sigma = crossprod(sigma)+ diag(rep(0.1, p))

# simulate multinormal data of sample size n  
sigsvd = svd(sigma)
Y = t(sigsvd$v %*% (t(sigsvd$u) * sqrt(sigsvd$d)))
X = matrix(rnorm(n * ncol(sigma)), nrow = n) %*% Y


# correlation shrinkage intensity
estimate.lambda(X) 
c = cor.shrink(X)
attr(c, "lambda")

# variance shrinkage intensity
estimate.lambda.var(X) 
v = var.shrink(X)
attr(v, "lambda.var")

corpcor documentation built on May 2, 2019, 2:51 p.m.