ApplyFdrCor: Applies multiple testing procedures built to control (asymptotically) the FDR for correlation testing.

Description

Applies multiple testing procedures built to control (asymptotically) the FDR for correlation testing. Some have no theoretical proofs for tests on a correlation matrix.

Usage

ApplyFdrCor(data, alpha = 0.05, stat_test = "empirical",
  method = "LCTnorm", Nboot = 1000, vect = FALSE)

Arguments

data

matrix of observations

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's procedure Benjamini & Hochberg (1995)'s and 'BHboot', Benjamini-Hochberg (1995)'s procedure with bootstrap evaluation of p-values

Nboot

number of iterations for bootstrap p-values evaluation

vect

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.

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 {
n <- 100
p <- 10
corr_theo <- diag(1,p)
data <- MASS::mvrnorm(n,rep(0,p),corr_theo)
alpha <- 0.05
res <- ApplyFdrCor(data,alpha,stat_test='empirical',method='LCTnorm')
# }