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

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

Description

CDF of Higher Criticism statitic under the null hypothesis.

Usage

phc(q, M, k0, k1, LS = F, ZW = F, onesided = FALSE)

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.
LS	- if LS = T, then method of Li and Siegmund (2015) will be implemented (for independence case only).
ZW	- if ZW = T, then approximation method of Zhang and Wu will be implemented.
onesided	- TRUE if the input p-values are one-sided.

Value

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

References

1. Hong Zhang, Jiashun Jin and Zheyang Wu. "Distributions and Statistical Power of Optimal Signal-Detection Methods In Finite Cases", submitted.

2. Donoho, David; Jin, Jiashun. "Higher criticism for detecting sparse heterogeneous mixtures". Annals of Statistics 32 (2004).

3. Li, Jian; Siegmund, David. "Higher criticism: p-values and criticism". Annals of Statistics 43 (2015).

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)

SetTest documentation built on May 1, 2019, 9:11 p.m.