maxTinftyCor: 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)).

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

`data`	matrix of observations
`alpha`	level of multiple testing (used if logical=TRUE)
`stat_test`	'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 empirical correlations used for quantile evaluation; optional, useful for oracle estimation and step-down
`vect`	if TRUE returns a vector of adjusted p-values, corresponding to `vectorize(cor(data))`; if FALSE, returns an array containing the adjusted p-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
`arr.ind`	if TRUE, returns the indexes of the significant correlations, with respect to level alpha

Returns

the adjusted p-values, 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_SD

 
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)
# adjusted p-values
res <- maxTinftyCor(data,stat_test='empirical',Nboot=1000)
round(res,2)
# significant correlations with level alpha:
alpha <- 0.05
whichCor(res<alpha)
# directly
res <- maxTinftyCor(data,alpha,stat_test='empirical',Nboot=1000,arr.ind=TRUE)