cv.thresPPP {bspcov}

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
)

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.

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).

Value

CVdf

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

Author(s)

Kwangmin Lee

References

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

See Also

thresPPP

Examples

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)