maxTinftyCor_SD: Multiple testing method of Drton & Perlman (2007) for...
In TestCor: FWER and FDR Controlling Procedures for Multiple Correlation Tests

Description Usage Arguments Value References See Also Examples

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

maxTinftyCor_SD(
  data,
  alpha = 0.05,
  stat_test = "empirical",
  Nboot = 1000,
  OmegaChap = covDcorNorm(cor(data), stat_test),
  vect = FALSE,
  logical = TRUE,
  arr.ind = FALSE
)

`data`	matrix of observations
`alpha`	level of multiple testing
`stat_test`	4 test statistics are available: 'empirical' √{n}abs(corr)* 'fisher' √{n-3}1/2\log( (1+corr)/(1-corr) ) 'student' √{n-2}abs(corr)/√(1-corr^2)* '2nd.order' √{n}mean(Y)/sd(Y)* with Y=(X_i-mean(X_i))(X_j-mean(X_j))
`Nboot`	number of iterations for Monte-Carlo quantile evaluation
`OmegaChap`	matrix of covariance of test statistics; 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 TRUE/FALSE values for each entry of the correlation matrix
`logical`	if TRUE, returns either a vector or a matrix where each element is equal to TRUE if the corresponding null hypothesis is rejected, and to FALSE if it is not rejected if FALSE, returns a list of successive p-values : element [[i+1]] of the list giving the p-values evaluated on the non-rejected hypothesis at step [[i]]; p-values are either as a vector or a list depending on `vect`
`arr.ind`	if TRUE, returns the indexes of the significant correlations, with respect to level alpha

Returns

logicals, equal to TRUE if the corresponding element of the statistic vector is rejected, as a vector or a matrix depending of the value of vect,
an array containing indexes \lbrace(i,j),\,i<j\rbrace for which correlation between variables i and j is significant, if arr.ind=TRUE.

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., Université Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.

ApplyFwerCor, maxTinftyCor

 
n <- 100
p <- 10
corr_theo <- diag(1,p)
corr_theo[1,3] <- 0.5
corr_theo[3,1] <- 0.5
data <- MASS::mvrnorm(n,rep(0,p),corr_theo)
alpha <- 0.05
# significant correlations:
maxTinftyCor_SD(data,alpha,stat_test='empirical', arr.ind=TRUE)
# successive p-values
res <- maxTinftyCor_SD(data,stat_test='empirical', logical=FALSE)
lapply(res,FUN=function(x){round(x,2)})
# succesive rejections
lapply(res,FUN=function(x){whichCor(x<alpha)})