摘要：This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. Th

摘要

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, Lp 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.

嘉宾介绍

Yingjie Feng is an associate professor at the School of Economics and Management, Tsinghua University. He specializes in econometrics, mathematical statistics and quantitative methods in social sciences, with particular interest in nonparametric and semiparametric theory and causal inference with panel data. Most of his work is motivated by empirical problems in applied economics and policy evaluation. His research has been published in leading journals such as American Economic Review, Annals of Statistics, Journal of the American Statistical Association and Review of Economics and Statistics.

Yingjie received his Ph.D. in Economics and M.A. in Statistics in 2019 from the University of Michigan. He also completed an M.A. in Economics in 2014 and a B.A. in Economics in 2011 at Peking University. Before joining Tsinghua University, he was a postdoctoral research associate at Princeton University.

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