SetTest (version 0.3.0)

test.bj: Multiple comparison test using Berk and Jones (BJ) statitics.

Description

Multiple comparison test using Berk and Jones (BJ) statitics.

Usage

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

Value

pvalue - the p-value of the Berk-Jones test.

bjstat - the Berk-Jones statistic.

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

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.

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.

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.bj for the definition of the statistic.

Examples

test.bj(runif(10), M=diag(10), k0=1, k1=10)
#When the input are statistics#
stat.test = rnorm(20)
p.test = 2*(1 - pnorm(abs(stat.test)))
test.bj(p.test, M=diag(20), k0=1, k1=10)