Generate null samples for Gaussian copula covariates via co-sufficient sampling

This function generates co-sufficient null samples of a given subset of variables for Gaussian copula covariates.

cosuff.g_copula.nulls(X, i2, n21, S, K, sigma_X.list_S, verbose = FALSE)

Arguments

X	a n by p matrix, containing all the covariates.
i2	index of inference samples
n21	number of batches, and the batch size will be \|i2\|/n21
S	a subset of covariates, for which null samples are constructed.
K	number of null replicates.
sigma_X.list_S	a list of length \|S\|, with each element being the variance of the conditional distribution of the multivariate Gaussian.
verbose	whether to show intermediate progress (default: FALSE).

nulls.list_S: a list of length |S| whose element is a (|i2|*K)-dimensional vector, which contains K set of null samples.

Zhang L, Janson L (2020). “Floodgate: Inference for Model-Free Variable Importance.” arXiv preprint arXiv:2007.01283.