weighted.LR: Weighted Lehmann-Romano Procedure
In FDX: False Discovery Exceedance Controlling Multiple Testing Procedures

Description Usage Arguments Details Value See Also Examples

Apply the weighted [wLR] procedure, with or without computing the critical values, to a set of p-values. Both arithmetic and geometric weighting are available.

weighted.LR(
  raw.pvalues,
  weights,
  alpha = 0.05,
  zeta = 0.5,
  weighting.method = "AM",
  critical.values = FALSE
)

wLR.AM(raw.pvalues, weights, alpha = 0.05, zeta = 0.5, critical.values = FALSE)

wLR.GM(raw.pvalues, weights, alpha = 0.05, zeta = 0.5, critical.values = FALSE)

`raw.pvalues`	vector of the raw observed p-values, as provided by the end user and before matching with their nearest neighbor in the CDFs supports.
`weights`	a numeric vector. Contains the weights of the p-values.
`alpha`	the target FDP, a number strictly between 0 and 1. For `*.fast` kernels, it is only necessary, if `stepUp = TRUE`.
`zeta`	the target probability of not exceeding the desired FDP, a number strictly between 0 and 1. If `zeta=NULL` (the default), then `zeta` is chosen equal to `alpha`.
`weighting.method`	a character string specifying whether to conduct arithmetic (`direction="AM"`, the default) or geometric weighting (`direction="GM"`) of p-values.
`critical.values`	a boolean. If `TRUE`, critical constants are computed and returned (this is computationally intensive).

wLR.AM and wLR.GM are wrapper functions for weighted.LR. The first one simply passes all its parameters to weighted.LR with weighting.method = "AM" and wLR.GM does the same with weighting.method = "GM".

A FDX S3 class object whose elements are:

`Rejected`	Rejected raw p-values.
`Indices`	Indices of rejected hypotheses.
`Num.rejected`	Number of rejections.
`Adjusted`	Adjusted p-values (only for step-down direction).
`Weighted`	Weighted p-values.
`Critical.values`	Critical values (if requested).
`Method`	A character string describing the used algorithm, e.g. 'Discrete Lehmann-Romano procedure (step-up)'.
`FDP.threshold`	FDP threshold `alpha`.
`Exceedance.probability`	Probability `zeta` of FDP exceeding `alpha`; thus, FDP is being controlled at level `alpha` with confidence `1 - zeta`.
`Weighting`	A character string describing the weighting method.
`Data$raw.pvalues`	The values of `raw.pvalues`.
`Data$weights`	The values of `weights`.
`Data$data.name`	The respective variable names of `raw.pvalues` and `pCDFlist`.

kernel, FDX-package, continuous.LR, continuous.GR, discrete.LR, discrete.GR, discrete.PB, weighted.GR, weighted.PB

# Construction of the p-values and their supports for weighted methods
raw.pvalues.weighted <- c(0.7389727, 0.1882310, 0.1302457, 0.9513677,
                         0.7592122, 0.0100559, 0.0000027, 0.1651034)
weights <- c(0.7947122, 1.2633867, 2.8097858, 2.2112801,
            2.3878654, 1.2389620, 2.3878654, 0.7947122)

wLR.AM.fast <- wLR.AM(raw.pvalues.weighted, weights)
summary(wLR.AM.fast)

wLR.AM.crit <- wLR.AM(raw.pvalues.weighted, weights, critical.values = TRUE)
summary(wLR.AM.crit)

wLR.GM.fast <- wLR.GM(raw.pvalues.weighted, weights)
summary(wLR.GM.fast)

wLR.GM.crit <- wLR.GM(raw.pvalues.weighted, weights, critical.values = TRUE)
summary(wLR.GM.crit)