test.phi: Multiple comparison test using phi-divergence statistics.
In SetTest: Group Testing Procedures for Signal Detection and Goodness-of-Fit

test.phi

R Documentation

Multiple comparison test using phi-divergence statistics.

Description

Multiple comparison test using phi-divergence statistics.

Usage

test.phi(prob, M, k0, k1, s = 2, onesided = FALSE, method = "ecc", ei = NULL)

Arguments

`prob`	- vector of input p-values.
`M`	- correlation matrix of input statistics (of the input p-values).
`k0`	- search range starts from the k0th smallest p-value.
`k1`	- search range ends at the k1th smallest p-value.
`s`	- phi-divergence parameter. s = 2 is the higher criticism statitic.s = 1 is the Berk and Jones statistic.
`onesided`	- TRUE if the input p-values are one-sided.
`method`	- default = "ecc": the effective correlation coefficient method in reference 2. "ave": the average method in reference 3, which is an earlier version of reference 2. The "ecc" method is more accurate and numerically stable than "ave" method.
`ei`	- the eigenvalues of M if available.

Value

pvalue - The p-value of the phi-divergence test.

phistat - phi-diergence statistic.

location - the order of the input p-values to obtain phi-divergence statistic.

References

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 3. Hong Zhang and Zheyang Wu. "Generalized Goodness-Of-Fit Tests for Correlated Data", arXiv:1806.03668. 4. Leah Jager and Jon Wellner. "Goodness-of-fit tests via phi-divergences". Annals of Statistics 35 (2007).

Examples

stat.test = rnorm(20) # Z-scores
p.test = 2*(1 - pnorm(abs(stat.test)))
test.phi(p.test, M=diag(20), s = 0.5, k0=1, k1=10)
test.phi(p.test, M=diag(20), s = 1, k0=1, k1=10)
test.phi(p.test, M=diag(20), s = 2, k0=1, k1=10)

SetTest documentation built on Sept. 12, 2024, 7:41 a.m.