SetTest (version 0.3.0)

phc: CDF of Higher Criticism statistic under the null hypothesis.

Description

CDF of Higher Criticism statistic under the null hypothesis.

Usage

phc(q, M, k0, k1, onesided = FALSE, method = "ecc", ei = NULL)

Value

The left-tail probability of the null distribution of HC statistic at the given quantile.

Arguments

q

- quantile, must be a scalar.

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.

See Also

stat.hc for the definition of the statistic.

Examples

pval <- runif(10)
hcstat <- stat.phi(pval, s=2, k0=1, k1=5)$value
phc(q=hcstat, M=diag(10), k0=1, k1=10)