stat.phi {SetTest}

Construct phi-divergence statistics.

Description

Construct phi-divergence statistics.

Usage

stat.phi(p, s, k0 = 1, k1 = NA)

Arguments

p

- vector of input p-values.

s

- phi-divergence parameter. s = 2 is the higher criticism statitic.s = 1 is the Berk and Jones statistic.

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 phi-divergence statistic

PHI = \sqrt{2n}/(s - s^2) \max_{1 \leq i\leq \lfloor \beta n \rfloor} (-1)^j \sqrt{1 - (i/n)^s (p_{(i)})^s - (1-i/n)^{(1-s)} * (1-p_{(i)})^{(1-s)}}

and when p_{(i)} > i/n, j = 1, otherwise j = 0.

Value

value - phi-divergence statistic constructed from a vector of p-values.

location - the order of the p-values to obtain phi-divergence statistic.

stat - vector of marginal phi-divergence statistics.

References

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

2. Jager, Leah; Wellner, Jon A. "Goodness-of-fit tests via phi-divergences". Annals of Statistics 35 (2007).

Examples

stat.phi(runif(10), s = 2)
#When the input are statistics#
stat.test = rnorm(20)
p.test = 1 - pnorm(stat.test)
stat.phi(p.test, s = 0.5, k0 = 2, k1 = 5)