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

Description

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

Usage

SimuFdr(corr_theo, n = 100, Nsimu = 1, alpha = 0.05,
  stat_test = "empirical", method = "LCTnorm", Nboot = 1000,
  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 'LCTnorm' and 'LCTboot', developped by Cai & Liu (2016), 'BH', traditional Benjamini-Hochberg (1995)'s procedure, and 'BHboot', Benjamini-Hochberg (1995)'s procedure with bootstrap evaluation of pvalues

Nboot

number of iterations for Monte-Carlo of bootstrap quantile evaluation

seed

seed for the Gaussian simulations

Value

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

References

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the royal statistical society. Series B (Methodological), 289-300.

Cai, T. T., & Liu, W. (2016). Large-scale multiple testing of correlations. Journal of the American Statistical Association, 111(513), 229-240.

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.

Examples

Run this code

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