SimuFwer_oracle: Simulates Gaussian data with a given correlation matrix and applies oracle MaxTinfty on the correlations.

Description

Simulates Gaussian data with a given correlation matrix and applies oracle MaxTinfty (i.e. Drton & Perlman (2007)'s procedure with the true correlation matrix) on the correlations.

Usage

SimuFwer_oracle(
  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

only 'MaxTinfty' available

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 values for fwer, fdr, sensitivity, specificity and accuracy.

References

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

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 <- 50
p <- 10
corr_theo <- diag(1,p)
corr_theo[1,3] <- 0.5
corr_theo[3,1] <- 0.5
alpha <- 0.05
SimuFwer_oracle(corr_theo,n,Nsimu,alpha,stat_test='empirical',stepdown=FALSE,Nboot=100)
# }