calculateBetaAdjustment: Calculating the beta adjustment factor for the asymptotically...

In mutoss: Unified Multiple Testing Procedures

Calculating the beta adjustment factor for the asymptotically optimal rejection curve.

Description

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.

Usage

calculateBetaAdjustment(n, startIDX_SUD, alpha, silent=FALSE,
    initialBeta=1, maxBinarySteps=50, tolerance=1e-04)

Arguments

n	Number of tests for which the adjusted beta should be calculated.
startIDX_SUD	Starting index of the step-up-down procedure
alpha	The level at which the FDR shall be controlled.
silent	If true any output on the console will be suppressed.
initialBeta	Initial beta.
maxBinarySteps	Maximum number of steps that will be performed.
tolerance	The tolerance to search for an upper FDR bound element in [alpha - tolerance, alpha]

Details

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.

Value

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.

Author(s)

MarselScheer

mutoss documentation built on March 31, 2023, 8:46 p.m.