pARI {pARI}

Permutation-based All-Resolutions Inference

Description

The main function for All-Resolutions Inference (ARI) method based on critical vectors constructed using the p-values permutation distribution. The function computes simultaneous lower bounds for the number of true discoveries for each set of hypotheses specified in ix controlling family-wise error rate.

Usage

pARI(X= NULL, ix, alpha = 0.05, family = "simes", delta = 0, B = 1000, pvalues = NULL, 
test.type = "one_sample", complete = FALSE, clusters = FALSE, iterative = FALSE, 
approx = TRUE, ncomb = 100, step.down = FALSE, max.step = 10, ...)

Arguments

X

data matrix where rows represent the m variables and columns the n observations.

ix

numeric vector which expresses the set of hypotheses of interest. It can be a vector with length equals m indicating the corresponding cluster for each variable, (in this case, you must put clusters = TRUE), or a vector containing the position indices of the variables of interest if only one set/cluster of hypotheses is considered.

alpha

numeric value in '[0,1]'. It expresses the alpha level to control the family-wise error rate.

family

string character. Choose a family of confidence envelopes to compute the critical vector from "simes", "aorc", "beta" and "higher.criticism".#' @param alpha alpha level.

delta

numeric value. It expresses the delta value, please see the references. Default to 0.

B

numeric value. Number of permutations, default to 1000.

pvalues

matrix of pvalues with dimensions m \times B used instead of the data matrix X. Default to @NULL.

test.type

character string. Choose a type of tests among "one_sample", i.e., one-sample t-test, or "two_samples", i.e., two-samples t-tests. Default "one_sample".

complete

Boolean value. If TRUE the sets of critical vectors and the raw pvalues are returned. Default @FALSE.

clusters

Boolean value. If ix indicates many clusters/sets must be TRUE. Default @FALSE.

iterative

Boolean value. If iterative = TRUE, the iterative method for improvement of confidence envelopes is applied. Default @FALSE.

approx

Boolean value. Default @TRUE. If you are treating high dimensional data, we suggest to put approx = TRUE to speed up the computation time.

ncomb

Numeric value. If approx = TRUE, you must decide how many random subcollections (level of approximation) considered.

step.down

Boolean value. Default @FALSE If you want to compute the lambda calibration parameter using the step-down approach put TRUE.

max.step

Numeric value. Default to 10. Maximum number of steps for the step down approach, so useful when step.down = TRUE.

...

Futher parameters.

Value

by default returns a list with the following objects: discoveries: lower bound for the number of true discoveries in the set selected, ix: selected variables. If complete = TRUE the raw pvalues and cv critical vector are returned.

Author(s)

Angela Andreella

References

For the general framework of All-Resolutions Inference see:

Goeman, Jelle J., and Aldo Solari. "Multiple testing for exploratory research." Statistical Science 26.4 (2011): 584-597.

For permutation-based All-Resolutions Inference see:

Andreella, Angela, et al. "Permutation-based true discovery proportions for fMRI cluster analysis." arXiv preprint arXiv:2012.00368 (2020).

See Also

The type of tests implemented: signTest permTest.

Examples

datas <- simulateData(pi0 = 0.8, m = 1000, n = 30, power = 0.9, rho = 0,seed = 123)
out <- pARI(X = datas, ix = c(1:200),test.type = "one_sample")
out