Select Tuning Parameter for Thresholding Covariance Matrix by CV

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Description

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

Usage

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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

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 "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

References

"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi

Examples

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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