bspcov (version 1.0.0)

cv.thresPPP: CV for Bayesian Estimation of a Sparse Covariance Matrix

Description

Performs cross-validation to estimate spectral norm error for a post-processed posterior of a sparse covariance matrix.

Usage

cv.thresPPP(
  X,
  thresvec,
  epsvec,
  prior = NULL,
  thresfun = "hard",
  nsample = 2000,
  ncores = 2
)

Value

CVdf

a M \(\times\) 3 dataframe having the estimated spectral norm error for each thres and eps, where M = length(thresvec) * length(epsvec)

Arguments

X

a n \(\times\) p data matrix with column mean zero.

thresvec

a vector of real numbers specifying the parameter of the threshold function.

epsvec

a vector of small positive numbers decreasing to \(0\).

prior

a list giving the prior information. The list includes the following parameters (with default values in parentheses): A (I) giving the positive definite scale matrix for the inverse-Wishart prior, nu (p + k) giving the degree of freedom of the inverse-Wishar prior.

thresfun

a string to specify the type of threshold function. fun ('hard') giving the thresholding function ('hard' or 'soft') for the thresholding PPP procedure.

nsample

a scalar value giving the number of the post-processed posterior samples.

ncores

a scalar value giving the number of CPU cores.

Author

Kwangmin Lee

Details

Given a set of train data and validation data, the spectral norm error for each \(\gamma\) and \(\epsilon_n\) is estimated as follows: $$ ||\hat{\Sigma}(\gamma,\epsilon_n)^{(train)} - S^{(val)}||_2 $$ where \(\hat{\Sigma}(\gamma,\epsilon_n)^{(train)}\) is the estimate for the covariance based on the train data and \(S^{(val)}\) is the sample covariance matrix based on the validation data. The spectral norm error is estimated by the \(10\)-fold cross-validation. For more details, see the first paragraph on page 9 in Lee and Lee (2023).

References

Lee, K. and Lee, J. (2023), "Post-processes posteriors for sparse covariances", Journal of Econometrics, 236(3), 105475.

See Also

thresPPP

Examples

# \donttest{
Sigma0 <- diag(1,50)
X <- mvtnorm::rmvnorm(25,sigma = Sigma0)
thresvec <- c(0.01,0.1)
epsvec <- c(0.01,0.1)
res <- bspcov::cv.thresPPP(X,thresvec,epsvec,nsample=100)
plot(res)# }
# \dontshow{
# R CMD check: make sure any open connections are closed afterward
if (!inherits(future::plan(), "sequential")) future::plan(future::sequential)
# }