mutoss (version 0.1-3)

aorc: Step-up-down test based on the asymptotically optimal rejection curve.

Description

Performs a step-up-down test on pValues. The critical values are based on the asymptotically optimal rejection curve. To have finite FDR control, an automatic adjustment of the critical values is done (see details for more).

Usage

aorc(pValues, alpha, startIDX_SUD=length(pValues), betaAdjustment,
    silent=FALSE)

Arguments

pValues

pValues to be used. They are assumed to be stochastically independent.

alpha

The level at which the FDR shall be controlled.

startIDX_SUD

The index at which critical value the step-up-down test starts. Default is length(pValues) and thus the function aorc() by default behaves like an step-up test.

betaAdjustment

A numeric value to adjust the asymptotically optimal rejection curve for the finite sample case. If betaAdjustment is not set an algorithm will calculate it, but this can be time-consuming.

silent

If true any output on the console will be suppressed.

Value

• A list containing:
• adjPValues
  A numeric vector containing the adjusted pValues
• rejected
  A logical vector indicating which hypotheses are rejected
• criticalValues
  A numeric vector containing critical values used in the step-up-down test
• errorControl
  A Mutoss S4 class of type errorControl, containing the type of error (FDR) controlled by the function and the level alpha.

Details

The graph of the function f(t) = t / (t * (1 - alpha) + alpha) is called the asymptotically optimal rejection curve. Denote by finv(t) the inverse of f(t). Using the critical values finv(i/n) for i = 1, ..., n yields asymptotic FDR control. To ensure finite control it is possible to adjust f(t) by a factor. The function calculateBetaAdjustment() calculates a beta such that (1 + beta / n) * f(t) can be used to control the FDR for a given finite sample size. If the parameter betaAdjustment is not provided, calculateBetaAdjustment() will be called automatically.

References

Finner, H., Dickhaus, T. & Roters, M. (2009). On the false discovery rate and an asymptotically optimal rejection curve. The Annals of Statistics 37, 596-618.

Examples

r <- c(runif(10), runif(10, 0, 0.01))
result <- aorc(r, 0.05)
result <- aorc(r, 0.05, startIDX_SUD = 1)  ## step-down
result <- aorc(r, 0.05, startIDX_SUD = length(r))  ## step-up}