DiscreteFDR (version 2.1.0)

DBY: The Discrete Benjamini-Yekutieli Procedure

Description

Applies the Discrete Benjamini-Yekutieli procedure, with or without computing the critical constants, to a set of \(p\)-values and their respective discrete supports.

Usage

DBY(test.results, ...)
# S3 method for default
DBY(
  test.results,
  pCDFlist,
  alpha = 0.05,
  ret.crit.consts = FALSE,
  select.threshold = 1,
  pCDFlist.indices = NULL,
  ...
)
# S3 method for DiscreteTestResults
DBY(
  test.results,
  alpha = 0.05,
  ret.crit.consts = FALSE,
  select.threshold = 1,
  ...
)

Value

A DiscreteFDR 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.constants

critical values (only exists if computations where performed with ret.crit.consts = TRUE).

Data

list with input data.

Data$Method

character string describing the used algorithm, e.g. 'Discrete Benjamini-Hochberg procedure (step-up)'

Data$Raw.pvalues

observed \(p\)-values.

Data$pCDFlist

list of the \(p\)-value supports.

Data$FDR.level

FDR level alpha.

Data$Data.name

the respective variable names of the input data.

Select

list with data related to \(p\)-value selection; only exists if select.threshold < 1.

Select$Threshold

\(p\)-value selection threshold (select.threshold).

Select$Effective.Thresholds

results of each \(p\)-value CDF evaluated at the selection threshold.

Select$Pvalues

selected \(p\)-values that are \(\leq\) selection threshold.

Select$Indices

indices of \(p\)-values \(\leq\) selection threshold.

Select$Scaled

scaled selected \(p\)-values.

Select$Number

number of selected \(p\)-values \(\leq\) selection threshold.

Arguments

test.results

either a numeric vector with \(p\)-values or an R6 object of class DiscreteTestResults from package DiscreteTests for which a discrete FDR procedure is to be performed.

...

further arguments to be passed to or from other methods. They are ignored here.

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.

alpha

single real number strictly between 0 and 1 indicating the target FDR level.

ret.crit.consts

single boolean specifying whether critical constants are to be computed.

select.threshold

single real number strictly between 0 and 1 indicating the largest raw \(p\)-value to be considered, i.e. only \(p\)-values below this threshold are considered and the procedures are adjusted in order to take this selection effect into account; if threshold = 1 (the default), all raw \(p\)-values are selected.

pCDFlist.indices

list of numeric vectors containing the test indices that indicate to which raw \(p\)-value each unique support in pCDFlist belongs; ignored if the lengths of test.results and pCDFlist are equal.

Details

Computing critical constants (ret.crit.consts = TRUE) requires considerably more execution time, especially if the number of unique supports is large. We recommend that users should only have them calculated when they need them, e.g. for illustrating the rejection set in a plot or other theoretical reasons.

References

Döhler, S. (2018). A discrete modification of the Benjamini–Yekutieli procedure. Econometrics and Statistics, 5, pp. 137-147. tools:::Rd_expr_doi("10.1016/j.ecosta.2016.12.002")

See Also

discrete.BH(), DBH(), ADBH(), DBR()

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

# Compute p-values and their supports of Fisher's exact test
test.result <- generate.pvalues(df, "fisher")
raw.pvalues <- test.result$get_pvalues()
pCDFlist <- test.result$get_pvalue_supports()

# DBY without critical values; using test results object
DBY.fast <- DBY(test.result)
summary(DBY.fast)

# DBY with critical values; using extracted p-values and supports
DBY.crit <- DBY(raw.pvalues, pCDFlist, ret.crit.consts = TRUE)
summary(DBY.crit)