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

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

cosuff.gaussian.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.
verbose	whether to show intermediate progress (default: FALSE).

Value

A list of three objects. nulls.list_S: a list of length |S| whose element is a (|i2|*K)-dimensional vector, which contains K set of null samples; cosuf.X_proj.list: a list of length |S| whose element is E(Xij|X-ij,Tm) for i in the m-th batch; cosuf.sigma_X.list:a list of length |S| whose element is Var(Xij|X-ij,Tm).

References

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

See also

Other sampling: cosuff.g_copula.nulls(), sample.g_copula.nulls(), sample.gaussian.nulls()