Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions
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arXiv
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| Natura: | Preprint |
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2025
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| author | Derumigny, Alexis Girard, Lucas Guyonvarch, Yannick |
| author_facet | Derumigny, Alexis Girard, Lucas Guyonvarch, Yannick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions Derumigny, Alexis Girard, Lucas Guyonvarch, Yannick Statistics Theory Econometrics 62G15, 62J05 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. |
| title | Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions |
| topic | Statistics Theory Econometrics 62G15, 62J05 |
| url | https://arxiv.org/abs/2507.16776 |