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