kernel {FDX}

Kernel functions

Description

Kernel functions transform observed p-values or their support according to [HLR], [PB] and [HGR]. The output is used by discrete.LR, discrete.PB and discrete.GR, respectively. For each procedure, there is a kernel for fast computation and one for calculation of critical values. Kernels followed by ".crit", e.g. kernel.DGR.crit, compute and return these critical values, while kernels ending in ".fast" only transform p-values and are therefore faster. The end user should not use these functions directly.

Usage

kernel_DLR_fast(
  pCDFlist,
  pvalues,
  adaptive = TRUE,
  alpha = 0.05,
  stepUp = FALSE,
  zeta = 0.5,
  support = 0L
)

kernel_DLR_crit(
  pCDFlist,
  pvalues,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  zeta = 0.5,
  stepUp = FALSE
)

kernel_DGR_fast(pCDFlist, pvalues, adaptive = TRUE, alpha = 0.05)

kernel_DGR_crit(
  pCDFlist,
  pvalues,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  zeta = 0.5
)

kernel_DPB_fast(pCDFlist, pvalues, adaptive = TRUE, alpha = 0.05, exact = TRUE)

kernel_DPB_crit(
  pCDFlist,
  pvalues,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  zeta = 0.5,
  exact = TRUE
)

kernel_wLR_fast(qvalues, weights, alpha = 0.05, geom_weighting = FALSE)

kernel_wGR_fast(qvalues, weights, alpha = 0.05, geom_weighting = FALSE)

kernel_wPB_fast(
  qvalues,
  weights,
  alpha = 0.05,
  geom_weighting = FALSE,
  exact = TRUE
)

Arguments

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.

pvalues

a numeric vector. Contains all values of the p-values supports if we search for the critical constants. If not, contains only the observed p-values. Must be sorted in increasing order!

adaptive

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

alpha

the target FDP, a number strictly between 0 and 1. For *.fast kernels, it is only necessary, if stepUp = TRUE.

stepUp

a numeric vector. Identical to pvalues for a step-down procedure. Equals c.m for a step-up procedure.

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.

support

a numeric vector. Contains all values of the p-values supports. Ignored, if stepUp = FALSE. Must be sorted in increasing order!

sorted_pv

a vector of observed p-values, in increasing order.

exact

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

qvalues

a numeric vector. Contains weighted raw p-values.

weights

a numeric vector. Contains the weights of the p-values.

geom_weighting

a boolean specifying whether to conduct geometric (TRUE) or arithmetic (FALSE) weighting.

Value

For ".fast" kernels, a vector of transformed p-values is returned; ".crit" kernels return a list object with critical constants ($crit.consts) and transformed p-values ($pval.transf).

See Also

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

alpha <- 0.05

# If not searching for critical constants, we use only the observed p-values
sorted.pvals <- sort(raw.pvalues)
y.DLR.fast <- kernel_DLR_fast(pCDFlist, sorted.pvals, TRUE)
y.NDGR.fast <- kernel_DGR_fast(pCDFlist, sorted.pvals, FALSE)$pval.transf
# transformed values
y.DLR.fast
y.NDGR.fast

# compute support
pv.list <- sort(unique(unlist(pCDFlist)))
y.DGR.crit <- kernel_DGR_crit(pCDFlist, pv.list, sorted.pvals, TRUE)
y.NDPB.crit <- kernel_DPB_crit(pCDFlist, pv.list, sorted.pvals, FALSE)
# critical constants
y.DGR.crit$crit.consts
y.NDPB.crit$crit.consts
# transformed values
y.DGR.crit$pval.transf
y.NDPB.crit$pval.transf