Matias D. Cattaneo, Yingjie Feng, Boris Shigida
arXiv 9 Sep 2024 · Mathematics — Statistics Theory
arXiv:2409.05715 · PDF · DOI · OpenAlex · Extracted main text
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions; (ii) rate-optimal uniform Bahadur representations; (iii) rate-optimal uniform (and mean square) convergence rates; (iv) valid strong approximations and feasible uniform inference methods; and (v) extensions to functional transformations of underlying estimators. Uniformity is established over both the evaluation point of the nonparametric functional parameter and a Euclidean parameter indexing the class of loss functions. The results also account explicitly for the smoothness degree of the loss function (if any), and allow for a possibly non-identity (inverse) link function. We illustrate the theoretical and methodological results in four examples: quantile regression, distribution regression, $L_p$ regression, and Logistic regression. Many other possibly non-smooth, nonlinear, generalized, robust M-estimation settings are covered by our results. We provide detailed comparisons with the existing literature and demonstrate substantive improvements: we achieve the best (in some cases optimal) known results under improved (in some cases minimal) requirements in terms of regularity conditions and side rate restrictions. The supplemental appendix reports complementary technical results that may be of independent interest, including a novel uniform strong approximation result based on Yurinskii's coupling.
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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 | Belloni, Chernozhukov, Chetverikov and Kato (2015) Some New Asymptotic Theory for Least Squares Series: Pointwise and Uniform Results | 0.961 | 9 | 6 | 89% |
| 2 | Shang and Cheng (2013) Local and global asymptotic inference in smoothing spline models | 0.950 | 7 | 4 | 86% |
| 3 | Cattaneo and Farrell (2013) Optimal Convergence Rates, Bahadur Representation, and Asymptotic Normality of Partitioning Estimators | 0.941 | 6 | 4 | 83% |
| 4 | Cattaneo, Farrell and Feng (2020) Large Sample Properties of Partitioning-Based Series Estimators self | 0.866 | 20 | 10 | 65% |
| 5 | Belloni, Chernozhukov, Chetverikov and Fernandez-Val (2019) Conditional Quantile Processes based on Series or Many Regressors | 0.857 | 27 | 11 | 63% |
| 6 | Chen and Christensen (2015) Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions | 0.843 | 4 | 3 | 75% |
| 7 | Kong, Linton and Xia (2013) Global Bahadur representation for nonparametric censored regression quantiles and its applications | 0.811 | 4 | 2 | 100% |
| 8 | Cattaneo, Crump, Farrell and Feng (2024) On Binscatter | 0.737 | 4 | 4 | 50% |
| 9 | Huang (2003) Local Asymptotics for Polynomial Spline Regression | 0.737 | 3 | 3 | 67% |
| 10 | Chen and Kato (2020) Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications | 0.737 | 3 | 3 | 67% |
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