pARI (version 1.1.3)

dI: Lower bound for the number of true discoveries

Description

Calculates 1-\(\alpha\) lower confidence bound for the set-wise of false null hypotheses.

Usage

dI(ix, cv, pvalues, iterative, approx, ncomb, ...)

Value

Numeric value: the lower confidence bound for the number of true discoveries concerning the cluster ix specified.

Arguments

ix

Numeric vector: set-wise hypotheses considered.

cv

Numeric vector: critical vector computed by criticalVector.

pvalues

If iterative = TRUE you must put here the matrix of \(p\)-values with dimensions \(m \times B\) where \(m\) is the number of variables and \(B\) the number of permutations. Instead, if iterative = FALSE, you can put directly the vector of \(m\) observed \(p\)-values.

iterative

Boolean value. If iterative = TRUE, the iterative method is applied (computationally demanding). Default to FALSE. Please see the reference below.

approx

Boolean value. Default to TRUE. If you are analyzing high dimensional data, we suggest to put approx = TRUE to speed up the computation time. Please see the reference below.

ncomb

Numeric value. If approx = TRUE, you must decide how many random sub collections (level of approximation) considered. Default to 100.

...

Further arguments for the iterative approach, i.e., iterative = TRUE.

Author

Angela Andreella

References

Andreella, A., Hemerik, J., Finos, L., Weeda, W., & Goeman, J. (2023). Permutation-based true discovery proportions for functional magnetic resonance imaging cluster analysis. Statistics in Medicine, 42(14), 2311-2340.

Examples

db <- simulateData(pi0 = 0.7, m = 100, n = 20, rho = 0)
out <- signTest(X = db)
pv <- cbind(out$pv, out$pv_H0)
cv <- criticalVector(pvalues = pv, family = "simes", lambda = 0.1, alpha = 0.1)
dI(ix = c(1:100), cv = cv, pvalues = pv)