ApplyFwerCor_oracle: Applies an oracle version of MaxTinfty procedure described in Drton & Perlman (2007) for correlation testing.

Description

Applies oracle MaxTinfty procedure described in Drton & Perlman (2007) which controls asymptotically the FWER for tests on a correlation matrix. It needs the true correlation matrix.

Usage

ApplyFwerCor_oracle(data, corr_theo, alpha = 0.05,
  stat_test = "empirical", method = "MaxTinfty", Nboot = 1000,
  stepdown = TRUE, vect = FALSE)

Arguments

data

matrix of observations

corr_theo

true matrix of corrlations

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' implemented

Nboot

number of iterations for Monte-Carlo of bootstrap quantile evaluation

stepdown

logical, if TRUE a stepdown procedure is applied if FALSE, returns an array containing rows and columns of significative correlations

vect

optional, logical, if TRUE returns a vector of TRUE/FALSE values, corresponding to vectorize(cor(data)); if FALSE, returns an array containing rows and columns of significative correlations

Value

Returns the list of significative correlations according to the multiple testing procedure applied Oracle estimation of the quantile is used, based on the true correlation matrix

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 {
n <- 100
p <- 10
corr_theo <- diag(1,p)
data <- MASS::mvrnorm(n,rep(0,p),corr_theo)
alpha <- 0.05
res <- ApplyFwerCor_oracle(data,corr_theo,alpha,stat_test='empirical',Nboot=1000,stepdown=FALSE)
# }