banded.chol.cv {FastBandChol}

Selects bandwidth for Cholesky factorization by cross validation

Description

Selects bandwidth for Cholesky factorization by k-fold cross validation

Usage

banded.chol.cv(X, bandwidth, folds = 3, est.eval = TRUE, Frob = TRUE)

Arguments

X

A data matrix with n rows and p columns. Rows are assumed to be independent realizations from a p-variate distribution with covariance \Sigma.

bandwidth

A vector of candidate bandwidths. Candidate bandwidths can only positive integers such that the maximum is less than the sample size outside of the kth fold.

folds

The number of folds used for cross validation. Default is folds =3.

est.eval

Logical: est.eval = TRUE returns a list with both the selected bandwidth and the estimated covariance matrix. est.eval=FALSE returns a list with only the selected bandwidth. The default is est.eval = TRUE.

Frob

Logical: Frob = TRUE uses squared Frobenius norm loss for cross-validation. Frob = FALSE uses operator norm loss. Default is Frob = TRUE.

Value

a list with

bandwidth.min

The bandwidth minimizing cross-validation error.

est

The estimated covariance matrix computed with bandwidth=bandwidth.min.

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))

## perform cross validation
k = 4:7
out1.cv = banded.chol.cv(X, bandwidth=k, folds = 5)