FinCovRegularization (version 1.1.0)

threshold.cv: Select Tuning Parameter for Thresholding Covariance Matrix by CV

Description

Apply K-fold cross-validation for selecting tuning parameters for thresholding covariance matrix using grid search strategy

Usage

threshold.cv(matrix, method = "hard", thresh.len = 20, n.cv = 10, norm = "F", seed = 142857)

Arguments

matrix

a N*p matrix, N indicates sample size and p indicates the dimension

method

thresholding method, "hard" or "soft"

thresh.len

the number of thresholding values tested in cross-validation, the thresholding values will be a sequence of thresh.len equally spaced values from minimum threshold constant to largest covariance in sample covariance matrix

n.cv

times that cross-validation repeated, the default number is 10

norm

the norms used to measure the cross-validation errors, which can be the Frobenius norm "F" or the operator norm "O"

seed

random seed, the default value is 142857

Value

An object of class "CovCv" containing the cross-validation's result for covariance matrix regularization, including:

regularization

regularization method, which is "Hard Thresholding" or "Soft Thresholding"

parameter.opt

selected optimal parameter by cross-validation

cv.error

the corresponding cross-validation errors

n.cv

times that cross-validation repeated

norm

the norm used to measure the cross-validation error

seed

random seed

threshold.grid

thresholding values tested in cross-validation

Details

For cross-validation, this function split the sample randomly into two pieces of size n1 = n-n/log(n) and n2 = n/log(n), and repeat this k times

References

"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi

Examples

data(m.excess.c10sp9003)
retcov.cv <- threshold.cv(m.excess.c10sp9003, method = "hard",
                          thresh.len = 20, n.cv = 10, norm = "F", seed = 142857)
summary(retcov.cv)
plot(retcov.cv)
# Low dimension