weighted.PB {FDX}

Weighted Poisson-Binomial Procedure

Description

Apply the weighted [wPB] procedure, with or without computing the critical values, to a set of p-values. Both arithmetic and geometric weighting are available. Additionally, the user can choose between exact computation of the Poisson-Binomial distribution or a refined normal approximation.

Usage

weighted.PB(
  raw.pvalues,
  weights,
  alpha = 0.05,
  zeta = 0.05,
  weighting.method = "AM",
  critical.values = FALSE,
  exact = TRUE
)

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

wPB.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).

exact

a boolean specifying whether to compute the Poisson-Binomial distribution exactly or by a normal approximation.

Details

wPB.AM and wPB.GM are wrapper functions for weighted.PB. The first one simply passes all its parameters to weighted.PB with weighting.method = "AM" and wPB.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.

See Also

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

Examples

# 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)

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

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

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

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