test.phi {SetTest}

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).

See Also

stat.phi for the definition of the statistic.v

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)