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Construct phi-divergence statistics.
stat.phi(p, s, k0 = 1, k1 = NA)
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.
- vector of input p-values.
- phi-divergence parameter. s = 2 is the higher criticism statitic.s = 1 is the Berk and Jones statistic.
- search range left end parameter. Default k0 = 1.
- 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 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 \(j = 0\).
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).
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)
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