标题： 凸成对差分估计量的稳健推断 显示英文标题

标题： Robust Inference for Convex Pairwise Difference Estimators

摘要： 本文开发了分布理论和基于自助法的推断方法，适用于广泛的一类凸成对差分估计量。这些估计量在观察对之间最小化一个核加权的参数凸函数，这些观察对在某些协变量方面相似，其中相似性由一个局部化（带宽）参数控制。虽然经典结果在严格的带宽条件下建立了渐近正态性，但我们表明，在更弱的假设下，有效的高斯和基于自助法的推断仍然是可能的。首先，我们将小带宽渐近理论扩展到凸成对估计设置中，即使使用比标准更小的带宽，也能得到稳健的高斯近似。其次，我们采用基于广义刀切法的去偏程序，以在保持目标函数凸性的同时，实现更大带宽的推断。第三，我们构建了一种新的自助方法，以调整带宽引起的方差扭曲，从而在广泛的带宽选择下实现有效的推断。我们提出的推断方法具有明显的鲁棒性，同时保留了凸成对差分估计量的实际吸引力。 显示英文摘要

摘要： This paper develops distribution theory and bootstrap-based inference methods for a broad class of convex pairwise difference estimators. These estimators minimize a kernel-weighted convex-in-parameter function over observation pairs that are similar in terms of certain covariates, where the similarity is governed by a localization (bandwidth) parameter. While classical results establish asymptotic normality under restrictive bandwidth conditions, we show that valid Gaussian and bootstrap-based inference remains possible under substantially weaker assumptions. First, we extend the theory of small bandwidth asymptotics to convex pairwise estimation settings, deriving robust Gaussian approximations even when a smaller than standard bandwidth is used. Second, we employ a debiasing procedure based on generalized jackknifing to enable inference with larger bandwidths, while preserving convexity of the objective function. Third, we construct a novel bootstrap method that adjusts for bandwidth-induced variance distortions, yielding valid inference across a wide range of bandwidth choices. Our proposed inference method enjoys demonstrable more robustness, while retaining the practical appeal of convex pairwise difference estimators.