Performing a fast exceedance control of the false discovery proportion(FDP)
under the framework proposed by Genovese, C., & Wasserman, L. (2004),
where FDP is defined by the number of false positives devided by the
number of total rejections.
The GW method requires an uniform(0,1) distributional test statistic
and each value in the input data represents a p-value from a hypothesis.
The sources of the data can be derived from any testing procedure
(e.g. pvalues from testing high-throughput gene data).
This function only supports specific uniform(0,1) distributional tests.
param_general_GW if you want a generic version of the GW method,
param_fast_GW( statistic = c("kth_p", "KS", "HC", "BJ", "Simes"), param1 = NULL, param2 = NULL, range_type = c("index", "proportion") )
character, the name of the statistic for the test, see details.
integer, the first parameter for the statistic, see details.
integer, the second parameter for the statistic, see details.
character, the type of the parameters, see details.
Note: We will use the term
pvalues interchangebly to refer
the data gathered by an inference procedure.
This function perform the fast GW algorithm, currently it supports the following test statistics:
kth_p: The kth pvalue statistic
KS: The Kolmogorov-Smirnov statistic
HC: The higher criticism statistic
BJ: The Berk-Jones statistic
For each statistic, you can specify the index of the ascending ordered samples
to control which data will be considered in the test statistics.
For example, the index of the kth pvalue statistic determines the value of
and use the kth smallest sample as its statistic.
similarly, the index of KS, HC and BJ determines which ordered samples
will be used to compute the test statistic.
range_type = "index", which means
the index. However, the index can also depend on the sample size. Therefore,
range_type = "proportion", The index is determined by the formula
n is the sample size.
For the kth pvalue statistic,
param1 determine the value of
k and must be
a single integer or a 0-1 value depending on
For KS, HC and BJ, the formula to decide the index is a little bit complicated.
range_type = "index",
param1 determines which
small sample(s) will be considered as the evidence of significance.
For example, if
param1 = 2 and the second smallest sample is significantly small,
it can lead to a significant result. Conversely,
param2 determines which large sample(s) can be treated as significance.
param2 can be a vector of integer. By default,
param2 are null, it is equivalent to
param1 = c(0, 1),
param2 = NULL and
range_type = "proportion".
range_type = "proportion",
param2 can be length 1 vectors,
which will be explained as the index from
max(floor(n*param),1), or they can
be length 2 vectors, where the index ranges from
an exceedance_parameters object
## The 3rd pvalue statistic param_fast_GW(statistic = "kth_p", param1 = 3) ## One-sided KS statistic param_fast_GW(statistic = "KS", param1 = c(0,1), range_type = "proportion") ## One-sided KS statistic, ## Test first 10 smallest pvalues only param_fast_GW(statistic = "KS", param1 = 1:10, range_type = "index")
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