stat.hc: Construct Higher Criticism (HC) statitics.
In SetTest: Group Testing Procedures for Signal Detection and Goodness-of-Fit

Description Usage Arguments Details Value References Examples

Construct Higher Criticism (HC) statitics.

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

`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.

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

HC = √{n} \max_{1 ≤q i≤q \lfloor β n \rfloor} [i/n - p_{(i)}] /√{p_{(i)}(1 - p_{(i)})}

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.

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).

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)

$value
[1] 1.790918

$location
[1] 4

$stat
[1] 0.4241360 0.9540402 1.3412361 1.7909180 1.7230540

$value
[1] 0.7533994

$location
[1] 4

$stat
 [1]  0.488294132 -0.000510022  0.633124555  0.753399435  0.188318875
 [6] -0.830271050 -0.472225766 -0.150326422 -0.027184679 -0.085744607