arXiv 16 Jul 2025 · Econometrics
arXiv:2507.12673 · PDF · DOI · OpenAlex · Extracted main text
This paper studies the semiparametric estimation and inference of integral functionals on submanifolds, which arise naturally in a variety of econometric settings. For linear integral functionals on a regular submanifold, we show that the semiparametric plug-in estimator attains the minimax-optimal convergence rate $n^{-\frac{s}{2s+d-m}}$, where $s$ is the H\"{o}lder smoothness order of the underlying nonparametric function, $d$ is the dimension of the first-stage nonparametric estimation, $m$ is the dimension of the submanifold over which the integral is taken. This rate coincides with the standard minimax-optimal rate for a $(d-m)$-dimensional nonparametric estimation problem, illustrating that integration over the $m$-dimensional manifold effectively reduces the problem's dimensionality. We then provide a general asymptotic normality theorem for linear/nonlinear submanifold integrals, along with a consistent variance estimator. We provide simulation evidence in support of our theoretical results.
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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 | –- and –- (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric iv regression | 0.941 | 6 | 4 | 83% |
| 2 | –- and Pouzo, D (2015) Sieve wald and qlr inferences on semi/nonparametric conditional moment models | 0.928 | 4 | 3 | 100% |
| 3 | –- and Reiss, M (2011) On rate optimality for ill-posed inverse problems in econometrics | 0.874 | 6 | 3 | 67% |
| 4 | –-, –- and Sun, Y (2014) Sieve inference on possibly misspecified semi-nonparametric time series models | 0.855 | 8 | 4 | 62% |
| 5 | –- (1993) Optimal rates of convergence of parameter estimators in the binary response model with weak distributional assumptions | 0.811 | 4 | 2 | 100% |
| 6 | Manski, C. F (1975) Maximum score estimation of the stochastic utility model of choice | 0.811 | 4 | 2 | 100% |
| 7 | Evans, L. C. and Gariepy, R. F (2015) Measure Theory and Fine Properties of Functions | 0.737 | 4 | 3 | 50% |
| 8 | –-, Chen, Z. and Gao, W. Y (2025) a) | 0.737 | 3 | 2 | 100% |
| 9 | Cattaneo, M. D., Titiunik, R. and Yu, R. R (2025) a) | 0.737 | 3 | 2 | 100% |
| 10 | –- and Liao, Z (2014) Sieve m inference on irregular parameters | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 56 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Boundary Discontinuity Designs: Theory and Practice | 0.843 | 3 | 3 |