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Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions

Alexis Derumigny, Lucas Girard, Yannick Guyonvarch

arXiv 22 Jul 2025 · Mathematics — Statistics Theory

arXiv:2507.16776 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
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6Shevtsova, I (2013) On the absolute constants in the berry–esseen inequality and its structural and nonuniform improvements0.64422100%
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10Pouliot, G. A (2024) An exact t-test, 20240.51121100%

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