Calculates the beta to adjust the asymptotically optimal rejection curve used by the function aorc() for a finite sample size. Then aorc(..., betaAdjustment = beta) controls the FDR also in the finite sample situation.
calculateBetaAdjustment(n, startIDX_SUD, alpha, silent=FALSE,
initialBeta=1, maxBinarySteps=50, tolerance=1e-04)The adjustment factor that is needed to ensure control of the FDR with the adjusted asymptotically optimal rejection curve at the specified level and sample size.
MarselScheer
Number of tests for which the adjusted beta should be calculated.
Starting index of the step-up-down procedure
The level at which the FDR shall be controlled.
If true any output on the console will be suppressed.
Initial beta.
Maximum number of steps that will be performed.
The tolerance to search for an upper FDR bound element in [alpha - tolerance, alpha]
The asymptotically optimal rejection curve, denoted by f(t), does not provide finite control of the FDR. calculateBetaAdjustment() calculates a factor, denoted by beta, such that (1 + beta/n) * f(t) provides finite control of the FDR.
The beta is calculated with the bisection approach. Assume there are beta1 and beta2 such that the choosing beta1 controls the FDR and beta2 not, then the optimal beta lies in [beta2, beta1]. If the choice (beta2 + beta1)/2 controls the FDR, the optimal FDR lies in [(beta2 + beta1)/2, beta1] and so on.