Efficient Estimation of Covariance and (Partial) Correlation
Description
This package implements a James-Stein-type shrinkage
estimator for the covariance matrix, with separate shrinkage
for variances and correlations. The details of the method are
explained in Sch\"afer and Strimmer (2005) and Opgen-Rhein and
Strimmer (2007). The approach is both computationally as well
as statistically very efficient, it is applicable to "small n,
large p" data, and always returns a positive definite and
well-conditioned covariance matrix. In addition to inferring
the covariance matrix the package also provides shrinkage
estimators for partial correlations, partial variances, and
regression coefficients. The inverse of the covariance and
correlation matrix can be efficiently computed, and as well as
any arbitrary power of the shrinkage correlation matrix.
Furthermore, functions are available for fast singular value
decomposition, for computing the pseudoinverse, and for
checking the rank and positive definiteness of a matrix.