ApplyFwerCor: Applies multiple testing procedures controlling (asymptotically) the FWER for tests on a correlation matrix.

Description

Applies multiple testing procedures controlling (asymptotically) the FWER for tests on a correlation matrix. Methods are described in Chapter 5 of roux.

Usage

ApplyFwerCor(data, alpha = 0.05, stat_test = "empirical",
  method = "MaxTinfty", Nboot = 1000, stepdown = TRUE,
  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 'Bonferroni', 'Sidak', 'BootRW', 'MaxTinfty'

Nboot

number of iterations for Monte-Carlo of bootstrap quantile evaluation

stepdown

logical, if TRUE a stepdown procedure is applied

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

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.

<U+0160>id<U+00E1>k, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62(318), 626-633.

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(data,alpha,stat_test='empirical',method='Bonferroni',stepdown=FALSE)
# }