arXiv 12 May 2026 · Econometrics
arXiv:2605.12284 · PDF · DOI · OpenAlex · Extracted main text
Conducting uniform inference on a continuous functional F defined on a compact subset X of R^d involves specifying L_n^d nodes for estimation and the construction of confidence bands. While asymptotically valid inference requires L_n to increase with n, existing fixed-L rules of thumb and heuristic data-driven approaches lack formal justification. This paper shows that, for functions within a Donsker class, the simple grid-growth condition r_n^(1/4)/L_n -> 0, equivalently L_n grows faster than r_n^(1/4), is sufficient for valid inference on twice continuously differentiable functions whose estimators satisfy r_n^(1/2)(F_hat - F) = O_p(1).
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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 | Chernozhukov, Victor and Fernández-Val, Iván and Melly, Blaise (2013) Inference on counterfactual distributions | 0.894 | 7 | 4 | 71% |
| 2 | Imai, Shunsuke (2025) Accuracy of Uniform Inference on Fine Grid Points | 0.644 | 2 | 2 | 100% |
| 3 | Kim, Doosoo and Wooldridge, Jeffrey M (2024) Difference-in-differences Estimator of Quantile Treatment Effect on the Treated | 0.511 | 2 | 2 | 50% |
| 4 | Meier, Jonas (2025) Multivariate distribution regression | 0.511 | 2 | 2 | 50% |
| 5 | Weiser, Alan and Zarantonello, Sergio E (1988) A note on piecewise linear and multilinear table interpolation in many dimensions | 0.511 | 2 | 2 | 50% |
| 6 | Kosorok, Michael R (2008) Introduction to empirical processes and semiparametric inference | 0.511 | 2 | 1 | 100% |
| 7 | Atkinson, Kendall and Han, Weimin (2009) Theoretical Numerical Analysis: A Functional Analysis Framework | 0.405 | 1 | 1 | 100% |
| 8 | Callaway, Brantly and Li, Tong (2019) Quantile treatment effects in difference in differences models with panel data | 0.405 | 1 | 1 | 100% |
| 9 | Epperson, James F (2013) An Introduction to Numerical Methods and Analysis | 0.405 | 1 | 1 | 100% |
| 10 | van der Vaart, Aad (2000) Asymptotic Statistics | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 11 scored citations.