qhc: Quantile of Higher Criticism statistics under the null...
In SetTest: Group Testing Procedures for Signal Detection and Goodness-of-Fit

View source: R/qhc.R

qhc	R Documentation

Quantile of Higher Criticism statistics under the null hypothesis.

Description

Quantile of Higher Criticism statistics under the null hypothesis.

Usage

qhc(p, M, k0, k1, onesided = FALSE, method = "ecc", ei = NULL, err_thr = 1e-04)

Arguments

`p`	- a scalar left probability that defines the quantile.
`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.
`err_thr`	- the error threshold. The default value is 1e-4.

Value

Quantile of HC statistics.

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.

Examples

## The 0.05 critical value of HC statistic when n = 10:
qhc(p=.95, M=diag(10), k0=1, k1=5, onesided=FALSE)
qhc(p=1-1e-5, M=diag(10), k0=1, k1=5, onesided=FALSE, err_thr=1e-8)

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