Uniform Estimation and Inference for Nonparametric Partitioning-Based M-Estimators
非参数分割型 M 估计的一致估计与统一推断
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…