FinCovRegularization (version 1.1.0)

tapering.cv: Select Tuning Parameter for Tapering Covariance Matrix by CV

Description

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

Usage

tapering.cv(matrix, h = 1/2, n.cv = 10, norm = "F", seed = 142857)

Arguments

matrix

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

h

the ratio between taper l_h and parameter l

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 "Tapering"

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

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 <- tapering.cv(m.excess.c10sp9003, n.cv = 10,
                         norm = "F", seed = 142857)
summary(retcov.cv)
plot(retcov.cv)
# Low dimension