To appear in AISTATS'23.

A short example on how to run simulations to evaluate our confidence intervals vs MLE as implemented by the glm() function in R.

source("simulations.R")
N = 1e4
p = 100
init_control = default_init(p)
init_control$gamma.method = "ipower"
out = parallel_sim(p, N, nreps=100, model="gaussian", sigma_x="id", init_control=init_control)

Output contains element-wise coverage, average coverage, and average interval length for our method and MLE.

• p controls the dimension.
• N controls the number of samples.
• nreps controls number of separate confidence intervals to generate, with newly generated data for each confidence interval.
• Set model to {gaussian, binomial, or poisson}.
• Set covariance matrix sigma_x to values {id, equicor, toeplitz, ill_cond}.
• To choose gamma selection method, set init_control$gamma.method to one of values {heuristic, bound, lmin, ipower}.