power.phi: Statistical power of phi-divergence test.

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

Description

Statistical power of phi-divergence test.

Usage

power.phi(alpha, n, s, beta, method = "gaussian-gaussian", eps = 0,
  mu = 0, df = 1, delta = 0)

Arguments

alpha	- type-I error rate.
n	- dimension parameter, i.e. the number of input statitics to construct phi-divergence statistic.
s	- phi-divergence parameter. s = 2 is the higher criticism statitic.s = 1 is the Berk and Jones statistic.
beta	- search range parameter. Search range = (1, beta*n). Beta must be between 1/n and 1.
method	- different alternative hypothesis, including mixtures such as, "gaussian-gaussian", "gaussian-t", "t-t", "chisq-chisq", and "exp-chisq". By default, we use Gaussian mixture.
eps	- mixing parameter of the mixture.
mu	- mean of non standard Gaussian model.
df	- degree of freedom of t/Chisq distribution and exp distribution.
delta	- non-cenrality of t/Chisq distribution.

Details

We consider the following hypothesis test,

H_0: X_i\sim F, H_a: X_i\sim G

Specifically, F = F_0 and G = (1-ε)F_0+ε F_1, where ε is the mixing parameter, F_0 and F_1 is speified by the "method" argument:

"gaussian-gaussian": F_0 is the standard normal CDF and F = F_1 is the CDF of normal distribution with μ defined by mu and σ = 1.

"gaussian-t": F_0 is the standard normal CDF and F = F_1 is the CDF of t distribution with degree of freedom defined by df.

"t-t": F_0 is the CDF of t distribution with degree of freedom defined by df and F = F_1 is the CDF of non-central t distribution with degree of freedom defined by df and non-centrality defined by delta.

"chisq-chisq": F_0 is the CDF of Chisquare distribution with degree of freedom defined by df and F = F_1 is the CDF of non-central Chisquare distribution with degree of freedom defined by df and non-centrality defined by delta.

"exp-chisq": F_0 is the CDF of exponential distribution with parameter defined by df and F = F_1 is the CDF of non-central Chisqaure distribution with degree of freedom defined by df and non-centrality defined by delta.

Value

Power of phi-divergence test.

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).

See Also

stat.phi for the definition of the statistic.

Examples

#If the alternative hypothesis Gaussian mixture with eps = 0.1 and mu = 1.2:#
power.phi(0.05, n=10, s=2, beta=0.5, eps = 0.1, mu = 1.2)

Example output

[1] 0.1537329

SetTest documentation built on May 1, 2019, 9:11 p.m.