ApplyFwerCor_oracle: Applies an oracle version of MaxTinfty procedure described in...
In TestCor: FWER and FDR Controlling Procedures for Multiple Correlation Tests

Description Usage Arguments Value References See Also Examples

Applies oracle MaxTinfty procedure described in Drton & Perlman (2007) which controls asymptotically the FWER for tests on a correlation matrix. It needs the true correlation matrix.

ApplyFwerCor_oracle(
  data,
  corr_theo,
  alpha = c(),
  stat_test = "empirical",
  method = "MaxTinfty",
  Nboot = 1000,
  stepdown = TRUE,
  vect = FALSE,
  logical = stepdown,
  arr.ind = FALSE
)

`data`	matrix of observations
`corr_theo`	true matrix of correlations
`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))
`method`	only 'MaxTinfty' implemented
`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 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 if `stepdown=TRUE` and `logical=FALSE`, returns a list of successive p-values.
`arr.ind`	if TRUE, returns the indexes of the significant correlations, with repspect to level alpha

Returns either

the adjusted p-values, as a vector or a matrix, depending on vect (unavailable with stepdown)
logicals indicating if the corresponding correlation is significant if logical=TRUE, as a vector or a matrix depending on 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.

Oracle estimation of the quantile is used, based on the true correlation matrix

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, 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 <- ApplyFwerCor_oracle(data,corr_theo,stat_test='empirical',Nboot=1000,stepdown=FALSE))
# significant correlations, level alpha:
alpha <- 0.05
whichCor(res<alpha)