Alexis Derumigny, Lucas Girard, Yannick Guyonvarch
arXiv 22 Jul 2025 · Mathematics — Statistics Theory
arXiv:2507.16776 · PDF · DOI · OpenAlex · Extracted main text
We contribute to bridging the gap between large- and finite-sample inference by studying confidence sets (CSs) that are both non-asymptotically valid and asymptotically exact uniformly (NAVAE) over semi-parametric statistical models. NAVAE CSs are not easily obtained; for instance, we show they do not exist over the set of Bernoulli distributions. We first derive a generic sufficient condition: NAVAE CSs are available as soon as uniform asymptotically exact CSs are. Second, building on that connection, we construct closed-form NAVAE confidence intervals (CIs) in two standard settings -- scalar expectations and linear combinations of OLS coefficients -- under moment conditions only. For expectations, our sole requirement is a bounded kurtosis. In the OLS case, our moment constraints accommodate heteroskedasticity and weak exogeneity of the regressors. Under those conditions, we enlarge the Central Limit Theorem-based CIs, which are asymptotically exact, to ensure non-asymptotic guarantees. Those modifications vanish asymptotically so that our CIs coincide with the classical ones in the limit. We illustrate the potential and limitations of our approach through a simulation study.
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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 | Derumigny, A., Girard, L., and Guyonvarch, Y (2023) Explicit non-asymptotic bounds for the distance to the first-order edgeworth expansion self | 1.000 | 6 | 3 | 100% |
| 2 | Romano, J. P., and Wolf, M (2000) Finite sample nonparametric inference and large sample efficiency | 0.811 | 4 | 2 | 100% |
| 3 | Kasy, M (2019) Uniformity and the delta method | 0.737 | 3 | 3 | 67% |
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| 6 | Shevtsova, I (2013) On the absolute constants in the berry–esseen inequality and its structural and nonuniform improvements | 0.644 | 2 | 2 | 100% |
| 7 | Peña, V., Lai, T., and Shao, Q (2008) Self-Normalized Processes: Limit Theory and Statistical Applications | 0.585 | 3 | 3 | 33% |
| 8 | Bahadur, R. R., and Savage, L. J (1956) The nonexistence of certain statistical procedures in nonparametric problems | 0.511 | 2 | 1 | 100% |
| 9 | D'Haultfuille, X., and Tuvaandorj, P (2024) A robust permutation test for subvector inference in linear regressions | 0.511 | 2 | 1 | 100% |
| 10 | Pouliot, G. A (2024) An exact t-test, 2024 | 0.511 | 2 | 1 | 100% |
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