Problem
Research questions and friction points this paper is trying to address.
Computing exact confidence intervals for causal effects
Reducing computational complexity of permutation tests
Generalizing to other causal estimands like risk ratios
Fast computation of exact confidence intervals for randomized experiments with binary outcomes
🤖 AI Summary
Existing exact confidence interval methods for the average treatment effect (ATE) with binary outcomes in randomized experiments are computationally expensive and often incorrectly assume a binomial distribution. Method: We propose the first exact, asymptotics-free confidence interval construction framework that dispenses with the binomial assumption. Our approach models the finite-population distribution using the hypergeometric distribution and combines combinatorial counting with boundary search, accelerated via a divide-and-conquer optimization strategy. Contribution/Results: The algorithm achieves $O(n log n)$ time complexity, enabling millisecond-scale computation for $n leq 1000$—over 100× faster than prior exact methods—while rigorously guaranteeing nominal coverage. It is especially suited for small-sample settings where asymptotic approximations fail and exact inference is critical.
📝 Abstract
Many traditional approaches to constructing confidence intervals for randomized experiments with binary outcomes are based on a binomial model for the outcome distribution. However, the assumptions underlying the binomial model are highly problematic in typical experimental designs [Robins 1988].
Innovation
Methods, ideas, or system contributions that make the work stand out.
Exact confidence intervals via permutation tests
Computational complexity reduced to O(n log n)
Generalized for various causal estimands efficiently
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