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

## Description

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.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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) ```

## Arguments

 `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).

## Details

`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"`.

## Value

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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# 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) ```