Bob Wilson
arXiv 3 Sep 2026 · Statistics — Methodology
arXiv:2609.03227 · PDF · Extracted main text
We give an exact randomization-based confidence set for the average treatment effect (ATE) in matched-pair studies with a binary outcome, requiring neither monotonicity nor any distributional assumption beyond the within-pair coin flip. At its core is an analytic solution to the worst-case allocation of attributable effects: two binomial-symmetry lemmas identify the pattern hardest to reject as a single boundary corner, so testing null hypotheses needs no integer program and no numerical search. Inverting the test via binary search yields a prediction set for the attributable effect in O(log S) Binomial tail calculations; the Bonferroni proposition of Rigdon and Hudgens (2015) produces the ATE confidence set at the same computational cost. The same corner extends without further machinery to a sensitivity analysis for matched observational studies under Rosenbaum's $Γ$-model. A simple formula for the design sensitivity illuminates when an observational study can hope to provide evidence for an effect.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Joseph Rigdon and Michael G Hudgens (2015) Randomization inference for treatment effects on a binary outcome | 1.000 | 6 | 4 | 100% |
| 2 | Paul R. Rosenbaum (2002) Attributing effects to treatment in matched observational studies | 0.843 | 3 | 3 | 100% |
| 3 | Paul R. Rosenbaum (2001) Effects attributable to treatment: Inference in experiments and observational studies with a discrete pivot | 0.737 | 3 | 2 | 100% |
| 4 | Joseph L Fleiss, Bruce Levin, and Myunghee Cho Paik (2013) Statistical methods for rates and proportions | 0.644 | 2 | 2 | 100% |
| 5 | J. L. Hodges and E. L. Lehmann (1963) Estimates of location based on rank tests | 0.644 | 2 | 2 | 100% |
| 6 | Erich L. Lehmann (1975) Nonparametrics: Statistical Methods Based on Ranks | 0.644 | 2 | 2 | 100% |
| 7 | Peter M Aronow, Haoge Chang, and Patrick Lopatto (2025) Fast computation of exact confidence intervals for randomized experiments with binary outcomes | 0.405 | 1 | 1 | 100% |
| 8 | Jiaxun Li, Jacob Spertus, and Philip B Stark (2025) Exact and conservative inference for the average treatment effect in stratified experiments with binary outcomes | 0.405 | 1 | 1 | 100% |
| 9 | Charles F. Manski (2003) Partial Identification of Probability Distributions | 0.405 | 1 | 1 | 100% |
| 10 | J. S. Maritz (1995) Distribution-Free Statistical Methods | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 20 scored citations.