sd.rtm.Rom: Extractor function for asymptotic sd[R_m/m] under selected FDP control method

Description

A function which extracts the asymptotic standard deviation for the postive call proportion, R_m/m, under the selected FDP control method from the supplied pwr object, which is the result of a call to the main function, pwrFDR.

Usage

sd.rtm.Rom(object)

Arguments

object

An object of class, pwr, which is the result of a call to the main function, pwrFDR

Value

Returns the asymptotic standard deviation of the significant call proportion, sd[R_m/m], as an un-named numeric.

Details

The siginificant call proportion (SCP), R_m/m, under the selected FDP control method, is directly related to the ensemble power, which in turn, is determined by the effect size for tests distributed under the alternative, the sample size, the proportion of tests which are distributed according to the alternative and the size, alpha, in the selected FDP control method. Its asymptotic standard error, e.g. the asymptotic standard deviation over the square root of the number of simultaneous tests, m, gives an indication of the range of values one can expect for the significant call proportion. The standard deviations of the ratios R_m/m, T_m/M_m, and V_m/R_m are used internally in control of the distribution of V_m/R_m for the BHCLT FDP control method, and in calculation of the tail probability power for T_m/M_m.

References

Izmirlian G. (2020) Strong consistency and asymptotic normality for quantities related to the Benjamini-Hochberg false discovery rate procedure. Statistics and Probability Letters; 108713, <doi:10.1016/j.spl.2020.108713>.

Izmirlian G. (2017) Average Power and $λ$ -power in Multiple Testing Scenarios when the Benjamini-Hochberg False Discovery Rate Procedure is Used. <arXiv:1801.03989>

Examples

Run this code

# NOT RUN {
  rslt.BHFDR  <- pwrFDR(effect.size=0.79, n.sample=46, r.1=0.05, alpha=0.15)
  rslt.Auto.1 <- pwrFDR(effect.size=0.79, n.sample=46, r.1=0.05, alpha=0.15, N.tests=51,
                       FDP.control.method="Auto")
  rslt.Auto.2 <- pwrFDR(effect.size=0.79, n.sample=46, r.1=0.05, alpha=0.15, N.tests=49,
                       FDP.control.method="Auto")

  ## Asymptotic standard deviation of positive call proportion under BHFDR
  sdrtmRomBHFDR  <- sd.rtm.Rom(rslt.BHFDR)

  ## Asymptotic standard deviation of positive call proportion under BHCLT
  sdrtmRomAuto1 <- sd.rtm.Rom(rslt.Auto.1)

  ## Asymptotic standard deviation of positive call proportionunder Romano
  sdrtmRomAuto2 <- sd.rtm.Rom(rslt.Auto.2)
# }

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