A Grid-Rate Condition for Valid Uniform Inference
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916005460049920 |
|---|---|
| author | Tsyawo, Emmanuel Selorm |
| author_facet | Tsyawo, Emmanuel Selorm |
| contents | Estimating a continuous functional $F: \X \to \R$ involves specifying $L_n^d$ nodes on $\X \subset \R^d$ for estimation and uniform inference. 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 \(L_n=ω(r_n^{1/4})\) is sufficient for valid inference for twice continuously differentiable functions estimable at the \(r_n^{1/2}\) rate. This condition ensures that the approximation error is asymptotically negligible relative to the stochastic variation of the empirical process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Grid-Rate Condition for Valid Uniform Inference Tsyawo, Emmanuel Selorm Econometrics Estimating a continuous functional $F: \X \to \R$ involves specifying $L_n^d$ nodes on $\X \subset \R^d$ for estimation and uniform inference. 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 \(L_n=ω(r_n^{1/4})\) is sufficient for valid inference for twice continuously differentiable functions estimable at the \(r_n^{1/2}\) rate. This condition ensures that the approximation error is asymptotically negligible relative to the stochastic variation of the empirical process. |
| title | A Grid-Rate Condition for Valid Uniform Inference |
| topic | Econometrics |
| url | https://arxiv.org/abs/2605.12284 |