Simulate Gaussian test statistics

Usage

gaussianTestStatistics(
  m,
  B,
  pi0 = 1,
  SNR = 0,
  dep = c("equi", "Toeplitz"),
  param = 0
)

Arguments

m: Number of hypotheses
B: Number of simulations
pi0: Proportion of true null hypotheses
SNR: Signal to noise ratio. Either a numeric value (a measure of distance between H0 and H1) or a vector of length m*(1-pi0)
dep: A character value, the type of dependency between test statistics. Can be one of "equi" for equi-correlation, or "Toeplitz". Defaults to "equi".
param: A numeric value defaulting to 0. If dep=="equi", param is the level of equi-correlation between pairs of variables. If dep=="Toeplitz", the first row of the Toeplitz matrix will be (1:m)^(param).

Value

A list with elements

x: A vector of length \(m\) test statistics
X0: An \(m x B\) matrix of test statistics under the null hypothesis
H: A vector of length \(m\), the status of each hypothesis: 0 for true null hypothesis, and 1 for true alternative hypothesis

Details

Author

Gilles Blanchard, Pierre Neuvial and Etienne Roquain

Examples


m <- 123
B <- 100

# independent statistics under the full null
sim <- gaussianTestStatistics(m, B)

# equi-correlated statistics under the full null
sim <- gaussianTestStatistics(m, B, dep = "equi", param = 0.2)

# equi-correlated statistics with some signal
sim <- gaussianTestStatistics(m, B, pi0 = 0.8, SNR = 1, dep = "equi", param = 0.2)

## show test statistics
stat <- sim$x
pch <- 20
colStat <- 1+sim$H
plot(stat, col=colStat, main="Test statistics", pch=pch)
legend("topleft", c("H0", "H1"), pch=pch, col=1:2)


# Toeplitz statistics with some signal
sim <- gaussianTestStatistics(m, B, pi0 = 0.8, SNR = 1, dep = "Toeplitz", param = -0.5)