tapering.cv {FinCovRegularization}

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

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

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

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