PDSCE (version 1.0)

band.chol: Computes the banded covariance estimator by banding the covariance Cholesky factor

Description

Computes the $k$-banded covariance estimator by $k$-banding the covariance Cholesky factor as described by Rothman, Levina, and Zhu (2010).

Usage

band.chol(x, k, centered = FALSE, method = c("fast", "safe"))

Value

The banded covariance estimate (a $p$ by $p$ matrix).

Details

method="fast" is much faster than method="safe". See Rothman, Levina, and Zhu (2010).

References

Rothman, A. J., Levina, E., and Zhu, J. (2010). A new approach to Cholesky-based covariance regularization in high dimensions. Biometrika 97(3): 539-550.

See Also

band.chol.cv

Examples

set.seed(1)
n=10
p=20
true.cov=diag(p)
true.cov[cbind(1:(p-1), 2:p)]=0.4
true.cov[cbind(2:p, 1:(p-1))]=0.4
eo=eigen(true.cov, symmetric=TRUE)
z=matrix(rnorm(n*p), nrow=n, ncol=p)
x=z%*% tcrossprod(eo$vec*rep(eo$val^(0.5), each=p),eo$vec)
sigma=band.chol(x=x, k=1)
sigma