Asymptotically Unbiased Two-Sided DP-UMP Tests

Asymptotically Unbiased Two-Sided DP-UMP Tests

umpuApprox(theta, size, alpha, epsilon, delta)

Arguments

theta	The success probability for each trial (parameter \(\theta\) in Binomial(n, \(\theta\)))
size	The number of trials in Binomial distribution (parameter n in Binomial(n, \(\theta\)))
alpha	Level of the tests
epsilon	Parameter \(\epsilon\) in \((\epsilon, \delta)\)-DP
delta	Parameter \(\delta\) in \((\epsilon, \delta)\)-DP

Value

A vector of asymptotically unbiased two-sided DP-UMP tests

References

Awan, Jordan Alexander, and Aleksandra Slavkovic. 2020. "Differentially Private Inference for Binomial Data". Journal of Privacy and Confidentiality 10 (1). https://doi.org/10.29012/jpc.725.

See also

Calculating simple and one-sided DP-UMP tests (umpLeft or umpRight) and unbiased two-sided DP-UMP tests (UMPU)

Examples

#Comparing unbiased DP-UMP tests obtained by umpuApprox and UMPU
asymp <- umpuApprox(theta = 0.4, size = 10, alpha = 0.05, epsilon = 1, delta = 0.01)
twoside <- UMPU(theta = 0.4, size = 10, alpha = 0.05, epsilon = 1, delta = 0.01)

#Plot the probability of rejecting the null hypothesis based on x
plot(asymp, type = "l", lwd = 1.5, col = "red", xlab = "x",
  ylab = "Phi (Probability of rejecting the null hypothesis)",
  main = "Unbiased DP-UMP Tests")
lines(twoside, type = "l", lwd = 1.5, lty = 2, col = "blue")
legend("topleft", legend=c("Asymptotically UMPU", "UMPU"),
  col=c("red", "blue"), lty=1:2, lwd = 1.5)