maxTinftyCor: Multiple testing method of Drton & Perlman (2007) for correlations.

Description

Multiple testing method based on the evaluation of quantile by simulation of observations from the asymptotic distribution (Drton & Perlman (2007)).

Usage

maxTinftyCor(data, alpha = 0.05, stat_test = "empirical",
  Nboot = 1000, OmegaChap = covDcorNorm(cor(data), stat_test),
  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': \(\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)\)

Notice that 'gaussian' is not available.

Nboot

number of iterations for Monte-Carlo quantile evaluation

OmegaChap

matrix of covariance of empirical correlations used for quantile evaluation; optional, useful for oracle estimation and step-down

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 a vector of logicals, equal to TRUE if the corresponding element of stat is rejected.

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 <- maxTinftyCor(data,alpha,stat_test='empirical',Nboot=1000)
# }