create.second_order {knockoff}

Second-order Gaussian knockoffs

Description

This function samples second-order multivariate Gaussian knockoff variables. First, a multivariate Gaussian distribution is fitted to the observations of X. Then, Gaussian knockoffs are generated according to the estimated model.

Usage

create.second_order(X, method = c("asdp", "equi", "sdp"), shrink = F)

Arguments

X

n-by-p matrix of original variables.

method

either "equi", "sdp" or "asdp" (default: "asdp"). This determines the method that will be used to minimize the correlation between the original variables and the knockoffs.

shrink

whether to shrink the estimated covariance matrix (default: F).

Details

If the argument shrink is set to T, a James-Stein-type shrinkage estimator for the covariance matrix is used instead of the traditional maximum-likelihood estimate. This option requires the package corpcor. See cov.shrink for more details.

Even if the argument shrink is set to F, in the case that the estimated covariance matrix is not positive-definite, this function will apply some shrinkage.

Value

A n-by-p matrix of knockoff variables.

References

Candes et al., Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection, arXiv:1610.02351 (2016). https://web.stanford.edu/group/candes/knockoffs/index.html

See Also

Other create: create.fixed(), create.gaussian()

Examples

set.seed(2022)
p=100; n=80; k=15
rho = 0.4
Sigma = toeplitz(rho^(0:(p-1)))
X = matrix(rnorm(n*p),n) %*% chol(Sigma)
nonzero = sample(p, k)
beta = 3.5 * (1:p %in% nonzero)
y = X %*% beta + rnorm(n)

# Basic usage with default arguments
result = knockoff.filter(X, y, knockoffs=create.second_order)
print(result$selected)

# Advanced usage with custom arguments
knockoffs = function(X) create.second_order(X, method='equi')
result = knockoff.filter(X, y, knockoffs=knockoffs)
print(result$selected)