SimuFwer: Simulates Gaussian data with a given correlation matrix and applies a FWER controlling procedure on the correlations.

Description

Simulates Gaussian data with a given correlation matrix and applies a FWER controlling procedure on the correlations.

Usage

SimuFwer(corr_theo, n = 100, Nsimu = 1, alpha = 0.05,
  stat_test = "empirical", method = "MaxTinfty", Nboot = 1000,
  stepdown = TRUE, seed = NULL)

Arguments

corr_theo

the correlation matrix of Gaussien data simulated

sample size

Nsimu

number of simulations

alpha

level of multiple testing

stat_test

'empirical': \(\sqrt{n}*abs(corr)\)
'fisher': \(\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )\)
'student': \(\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)\)
'gaussian': \(\sqrt{n}*mean(Y)/sd(Y)\) with \(Y=(X_i-mean(X_i))(X_j-mean(X_j))\)

method

choice between 'Bonferroni', 'Sidak', 'BootRW', 'MaxTinfty'

Nboot

number of iterations for Monte-Carlo of bootstrap quantile evaluation

stepdown

logical, if TRUE a stepdown procedure is applied

seed

seed for the Gaussian simulations

Value

Returns a line vector containing estimated fwer, estimated fdr, estimated power, estimated true discovery rate.

References

Bonferroni, C. E. (1935). Il calcolo delle assicurazioni su gruppi di teste. Studi in onore del professore salvatore ortu carboni, 13-60.

Drton, M., & Perlman, M. D. (2007). Multiple testing and error control in Gaussian graphical model selection. Statistical Science, 22(3), 430-449.

Romano, J. P., & Wolf, M. (2005). Exact and approximate stepdown methods for multiple hypothesis testing. Journal of the American Statistical Association, 100(469), 94-108.

Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Universit<U+00E9> Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.

Westfall, P.H. & Young, S. (1993) Resampling-based multiple testing: Examples and methods for p-value adjustment, John Wiley & Sons, vol. 279.

Examples

Run this code

# NOT RUN {
Nsimu <- 1000 
n <- 100
p <- 10
corr_theo <- diag(1,p)
alpha <- 0.05
res <- SimuFwer(corr_theo,n,Nsimu,alpha,stat_test='empirical',method='Bonferroni',stepdown=FALSE)
# }