FDX (version 2.0.0)

kernel: 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.

Note: As of version 2.0, these functions are purely internal functions! As a consequence, they have to be called directly via :::, e.g. FDX:::kernel_DGR_fast(). But users should not rely on them, as parameters (including their names, order, etc.) may be changed without notice!

Usage

kernel_DLR_fast(
  pCDFlist,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  stepUp = FALSE,
  zeta = 0.5,
  support = numeric(),
  pCDFcounts = NULL
)
kernel_DLR_crit(
  pCDFlist,
  support,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  zeta = 0.5,
  stepUp = FALSE,
  pCDFcounts = NULL
)
kernel_wLR_fast(sorted_w_pv, weights, alpha = 0.05, geom_weighting = FALSE)
kernel_DGR_fast(
  pCDFlist,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  pCDFcounts = NULL
)
kernel_DGR_crit(
  pCDFlist,
  support,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  zeta = 0.5,
  pCDFcounts = NULL
)
kernel_wGR_fast(sorted_w_pv, weights, alpha = 0.05, geom_weighting = FALSE)
kernel_DPB_fast(
  pCDFlist,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  exact = TRUE,
  pCDFcounts = NULL
)
kernel_DPB_crit(
  pCDFlist,
  support,
  sorted_pv,
  adaptive = TRUE,
  alpha = 0.05,
  zeta = 0.5,
  exact = TRUE,
  pCDFcounts = NULL
)
kernel_wPB_fast(
  sorted_w_pv,
  weights,
  alpha = 0.05,
  geom_weighting = FALSE,
  exact = TRUE
)

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).

Arguments

pCDFlist

list of the supports of the CDFs of the p-values; each list item must be a numeric vector, which is sorted in increasing order and whose last element equals 1.

sorted_pv

numeric vector containing the raw p-values, sorted in increasing order.

adaptive

single boolean indicating whether to conduct an adaptive procedure or not.

alpha

single real number strictly between 0 and 1 specifying the target FDP.

stepUp

single boolean specifying whether to conduct the step-up (TRUE) or step-down (FALSE; the default) version of the discrete Lehmann-Romano procedure.

zeta

single real number strictly between 0 and 1 specifying the target probability of not exceeding the desired FDP. If zeta = NULL (the default), then zeta is chosen equal to alpha.

support

numeric vector, sorted in increasing order, that contains the entirety of all observable values of the p-value supports; for kernel_DLR_fast(), it is ignored if stepUp = FALSE.

pCDFcounts

integer vector of counts that indicates to how many p-values each unique p-value distribution belongs.

sorted_w_pv

numeric vector containing the weighted p-values, sorted in increasing order.

weights

numeric vector containing the rescaled weights, sorted in decreasing order.

geom_weighting

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

exact

single boolean indicating whether to compute the Poisson-Binomial distribution exactly or by normal approximation.

See Also

FDX, 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 with Fisher's exact test
library(DiscreteTests)  # for Fisher's exact test
test.results <- fisher_test_pv(df)
raw.pvalues <- test.results$get_pvalues()
pCDFlist <- test.results$get_pvalue_supports()

alpha <- 0.05

# If not searching for critical constants, we use only the observed p-values
sorted.pvals <- sort(raw.pvalues)
y.DLR.fast <- FDX:::kernel_DLR_fast(pCDFlist, sorted.pvals, TRUE)
y.NDGR.fast <- FDX:::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 <- FDX:::kernel_DGR_crit(pCDFlist, pv.list, sorted.pvals, TRUE)
y.NDPB.crit <- FDX:::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