FastBandChol-package {FastBandChol}

Fast estimation of covariance matrix by banded Cholesky factor

Description

Fast and numerically stable estimation of covariance matrix by banding the Cholesky factor using a modified Gram-Schmidt algorithm implemented in RcppArmadilo. See <https://stat.umn.edu/~molst029> for details on the algorithm.

Details

Package:	FastBandChol
Type:	Package
Version:	0.1.0
Date:	2015-08-22
License:	GPL-2

Author(s)

Aaron Molstad

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.

Examples

## set sample size and dimension
n = 20
p = 100

## create covariance with AR1 structure
Sigma = matrix(0, nrow=p, ncol=p)
for(l in 1:p){
  for(m in 1:p){
    Sigma[l,m] = .5^(abs(l-m))
  }
}

## simulation Normal data
eo1 = eigen(Sigma)
Sigma.sqrt = eo1$vec%*%diag(eo1$val^.5)%*%t(eo1$vec)
X = t(Sigma.sqrt%*%matrix(rnorm(n*p), nrow=p, ncol=n))

## compute estimates
est.sample = banded.sample(X, bandwidth=4)$est
est.chol = banded.chol(X, bandwidth=4)$est