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.