{"ID":2891909,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.16776","arxiv_id":"2507.16776","title":"Can we have it all? Non-asymptotically valid and asymptotically exact confidence intervals for expectations and linear regressions","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.","short_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 se...","url_abs":"https://arxiv.org/abs/2507.16776","url_pdf":"https://arxiv.org/pdf/2507.16776v2","authors":"[\"Alexis Derumigny\",\"Lucas Girard\",\"Yannick Guyonvarch\"]","published":"2025-07-22T17:23:04Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"econ.EM\"]","methods":"[\"Variational Autoencoder\"]","has_code":false}