UMP: Calculating Simple and One-Sided DP-UMP Tests

In ttran2401/binomialDP: Differentially Private Inference for Binomial Data

Description

Calculating Simple and One-Sided DP-UMP Tests

Usage

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

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

Arguments

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

Value

A vector of one-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 unbiased two-sided DP-UMP tests (UMPU) and asymptotically unbiased two-sided DP-UMP tests (umpuApprox)

Examples

#leftUMP
left <- umpLeft(theta = 0.4, size = 10, alpha = 0.05, epsilon = 1, delta = 0.01)

#rightUMP
right <- umpRight(theta = 0.4, size = 10, alpha = 0.05, epsilon = 1, delta = 0.01)

#plot
plot(left, type = "l", main = "One-sided DP UMP",
     xlab = "x", ylab = "Phi (Probability of rejecting the null hypothesis)")
lines(right, lty = 2, col = "blue")
legend("left", legend=c("Left UMP", "Right UMP"), col=c("black", "blue"), lty=1:2, lwd = 1.5)

ttran2401/binomialDP documentation built on July 7, 2020, 1:18 a.m.