stat.bj {SetTest}

Construct Berk and Jones (BJ) statistics.

Description

Construct Berk and Jones (BJ) statistics.

Usage

stat.bj(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 Berk and Jones statistic

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

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

Value

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

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

stat - vector of marginal BJ 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).

3. Berk, R.H. & Jones, D.H. Z. "Goodness-of-fit test statistics that dominate the Kolmogorov statistics". Wahrscheinlichkeitstheorie verw Gebiete (1979) 47: 47.

Examples

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