stat.hc: Construct Higher Criticism (HC) statistics.

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

Construct Higher Criticism (HC) statistics.

Description

Construct Higher Criticism (HC) statistics.

Usage

stat.hc(p, k0 = 1, k1 = NA)

Arguments

p	- vector of input p-values.
k0	- search range left end parameter. Default k0 = 1.
k1	- search range right end parameter. Default k1 = 0.5*number of input p-values.

Details

Let p_{(i)}, i = 1,...,n be a sequence of ordered p-values, the higher criticism statistic

HC = \sqrt{n} \max_{1 \leq i\leq \lfloor \beta n \rfloor} [i/n - p_{(i)}] /\sqrt{p_{(i)}(1 - p_{(i)})}

Value

value - HC statistic constructed from a vector of p-values.

location - the order of the p-values to obtain HC statistic.

stat - vector of marginal HC statistics.

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).

Examples

stat.hc(runif(10))
#When the input are statistics#
stat.test = rnorm(20)
p.test = 1 - pnorm(stat.test)
stat.hc(p.test, k0 = 1, k1 = 10)

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