discrete.LR {FDX}

Discrete Lehmann-Romano procedure

Description

Apply the [DLR] procedure, with or without computing the critical values, to a set of p-values and their discrete support. Both step-down and step-up procedures can be computed and non-adaptive versions are available as well.

Usage

discrete.LR(
  raw.pvalues,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  direction = "sd",
  adaptive = TRUE,
  critical.values = FALSE
)

DLR(
  raw.pvalues,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  direction = "sd",
  critical.values = FALSE
)

NDLR(
  raw.pvalues,
  pCDFlist,
  alpha = 0.05,
  zeta = 0.5,
  direction = "sd",
  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.

pCDFlist

a list of the supports of the CDFs of the p-values. Each support is represented by a vector that must be in increasing order.

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.

direction

a character string specifying whether to conduct a step-up (direction="su", the default) or step-down procedure (direction="sd").

adaptive

a boolean specifying whether to conduct an adaptive procedure or not.

critical.values

a boolean. If TRUE, critical constants are computed and returned (this is computationally intensive).

Details

DLR and NDLR are wrapper functions for discrete.LR. The first one simply passes all its parameters to discrete.LR with adaptive = TRUE and NDLR does the same with adaptive = FALSE.

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).

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.

Data$raw.pvalues

The values of raw.pvalues.

Data$pCDFlist

The values of pCDFlist.

Data$data.name

The respective variable names of raw.pvalues and pCDFlist.

References

S. Döhler and E. Roquain (2019). Controlling False Discovery Exceedance for Heterogeneous Tests. arXiv:1912.04607v1.

See Also

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

Examples

X1 <- c(4, 2, 2, 14, 6, 9, 4, 0, 1)
X2 <- c(0, 0, 1, 3, 2, 1, 2, 2, 2)
N1 <- rep(148, 9)
N2 <- rep(132, 9)
Y1 <- N1 - X1
Y2 <- N2 - X2
df <- data.frame(X1, Y1, X2, Y2)
df

# Construction of the p-values and their supports (fisher.pvalues.support
# is from 'DiscreteFDR' package!)
df.formatted <- fisher.pvalues.support(counts = df, input = "noassoc")
raw.pvalues <- df.formatted$raw
pCDFlist <- df.formatted$support

DLR.sd.fast <- DLR(raw.pvalues, pCDFlist)
summary(DLR.sd.fast)
DLR.su.fast <- DLR(raw.pvalues, pCDFlist, direction = "su")
summary(DLR.su.fast)

DLR.sd.crit <- DLR(raw.pvalues, pCDFlist, critical.values = TRUE)
summary(DLR.sd.crit)
DLR.su.crit <- DLR(raw.pvalues, pCDFlist, direction = "su", critical.values = TRUE)
summary(DLR.su.crit)

NDLR.sd.fast <- NDLR(raw.pvalues, pCDFlist)
summary(NDLR.sd.fast)
NDLR.su.fast <- NDLR(raw.pvalues, pCDFlist, direction = "su")
summary(NDLR.su.fast)

NDLR.sd.crit <- NDLR(raw.pvalues, pCDFlist, critical.values = TRUE)
summary(NDLR.sd.crit)
NDLR.su.crit <- NDLR(raw.pvalues, pCDFlist, direction = "su", critical.values = TRUE)
summary(NDLR.su.crit)