Blanchard-Roquain (2008) step-up Procedure for arbitrary dependent p-Values Also proposed independently by Sarkar (2008)
BlaRoq(pValues, alpha, pii, silent=FALSE)A list containing:
A numeric vector containing the adjusted pValues
A logical vector indicating which hypotheses are rejected
A numeric vector containing critical values used in the step-up test
A Mutoss S4 class of type errorControl, containing the type of error controlled by the function and the level alpha.
GillesBlanchard,HackNiklas
pValues to be used. They can have arbitrary dependence.
the level at which the FDR should be controlled
Prior for the proportion of true null hypotheses, same size as pValues
if true any output on the console will be suppressed.
A generalization of the Benjamini-Yekutieli procedure, taking as an additional parameter a distribution pii on [1..k] (k is the number of hypotheses) representing prior belief on the number of hypotheses that will be rejected.
It is a step-up Procedure with critical values C_i defined as alpha/k times the sum for j in [1..i] of j*pii[j]. For any fixed prior pii, the FDR is controlled at level alpha for arbitrary dependence structure of the p-Values. The particular case of the Benjamini-Yekutieli step-up is recovered by taking pii[i] proportional to 1/i.
If pii is missing, a default prior distribution proportional to exp( -i/(0.15*k) ) is taken. It should perform better than the BY procedure if more than about 0.05 to 0.1 of hypotheses are rejected, and worse otherwise.
Note: the procedure automatically normalizes the prior pii to sum to one if this is not the case.
Blanchard, G. and Roquain, E. (2008). Two simple sufficient conditions for FDR control. Electronic Journal of Statistics, 2:963-992. Sarkar, S.K. (2008) On methods controlling the false discovery rate. Sankhya, Series A, 70:135-168.