stat.bj

Construct Berk and Jones (BJ) statistics.

It provides cumulative distribution function (CDF),
quantile, p-value, statistical power calculator and random number generator
for a collection of group-testing procedures, including the Higher Criticism
tests, the one-sided Kolmogorov-Smirnov tests, the one-sided Berk-Jones tests,
the one-sided phi-divergence tests, etc. The input are a group of p-values.
The null hypothesis is that they are i.i.d. Uniform(0,1). In the context of
signal detection, the null hypothesis means no signals. In the context of the
goodness-of-fit testing, which contrasts a group of i.i.d. random variables to
a given continuous distribution, the input p-values can be obtained by the CDF
transformation. The null hypothesis means that these random variables follow the
given distribution. For reference, see [1]Hong Zhang, Jiashun Jin and Zheyang Wu.
"Distributions and power of optimal signal-detection statistics in finite case",
IEEE Transactions on Signal Processing (2020) 68, 1021-1033; [2] Hong Zhang and Zheyang Wu.
"The general goodness-of-fit tests for correlated data", Computational Statistics &
Data Analysis (2022) 167, 107379.

Hong Zhang

SetTest

Group Testing Procedures for Signal Detection and
Goodness-of-Fit

stat.bj function

<dl><dt>p</dt>
<dd>- vector of input p-values.</dd>
<dt>k0</dt>
<dd>- search range left end parameter. Default k0 = 1.</dd>
<dt>k1</dt>
<dd>- search range right end parameter. Default k1 = 0.5*number of input p-values.</dd></dl>

Arguments

Construct Berk and Jones (BJ) statistics. — stat.bj

<dl>

<dt>p</dt>
<dd>- vector of input p-values.</dd>


<dt>k0</dt>
<dd>- search range left end parameter. Default k0 = 1.</dd>


<dt>k1</dt>
<dd>- search range right end parameter. Default k1 = 0.5*number of input p-values.</dd>

</dl>

stat.bj: Construct Berk and Jones (BJ) statistics.

Description

Usage

Value

Arguments

Details

References

Examples