AI 中文总结
针对2SLS易受少量观测值不当影响的问题，本文提出W-2SLS方法，在对抗污染下达到极小极大精确速率，构建了稳健推断与检验，且无污染时也有更好的有限样本偏差保证。
AI 中文摘要
由于2SLS基于样本均值构建，少量观测值会对估计和推断产生不成比例的影响。本文提出W-2SLS，这是一种可直接替代的简单稳健化方法，用分位数缩尾均值替代这些样本均值。我们在对抗污染下分析W-2SLS，该设定允许受污染观测值的身份和报告值依赖于已实现的干净样本，因此可适配针对性或策略性操纵。在有限的m阶矩下，W-2SLS达到极小极大精确速率ηₙ^(1−1/m)+n^(−1/2)，其中ηₙ是可被改动的观测值比例。匹配的下界确定了一致收敛、根-n估计以及与干净样本2SLS具有相同一阶律的中心高斯推断的精确污染阈值。当√n·ηₙ^(1−1/m)→0时，稳健性是一阶无代价的。我们还构建了可行的异方差稳健推断，以及在弱识别和对抗污染下有效的缩尾Anderson–Rubin检验。最后，即使没有污染，普通2SLS也可能存在较差的有限样本一致收敛性，而W-2SLS可提供经置信校准的次高斯偏差保证。
英文摘要
Because 2SLS is built from sample averages, a small number of observations can have a disproportionate effect on estimates and inference. We introduce W-2SLS, a simple drop-in robustification that replaces these averages by quantile-winsorized means. We analyze W-2SLS under adversarial contamination, which permits both the identities and the reported values of the contaminated observations to depend on the realized clean sample and therefore accommodates targeted or strategic manipulation. Under finite $m$-th moments, W-2SLS attains the minimax-sharp rate $η_{n}^{1-\frac1m}+n^{-1/2}$, where $η_n$ is the fraction of observations that may be altered. Matching lower bounds identify the exact contamination thresholds for uniform consistency, root-$n$ estimation, and centered Gaussian inference with the same first-order law as clean-sample 2SLS. When $\sqrt{n}η_{n}^{1-\frac1m}\to 0$ robustness is first-order free. We also construct feasible heteroskedasticity-robust inference and a winsorized Anderson--Rubin test valid under weak identification and adversarial contamination. Finally, even without contamination, ordinary 2SLS can have poor uniform finite-sample concentration, whereas W-2SLS admits confidence-calibrated sub-Gaussian deviation guarantees.
