Asymptotically linear estimators in semiparametric models achieve their point-estimation guarantees via a von Mises expansion in which a second-order remainder is declared negligible. Confidence intervals then treat the first-order influence-function term as the sole source of sampling variability. This reasoning is asymptotically exact but can fail materially in finite samples whenever the second-order remainder contributes variation of the same order as the influence-function variance -- a regime we call the \emph{near-boundary regime}, characterized by nuisance estimation operating at or near the product-rate threshold. We develop a general theory of inference for this regime. Our contributions are: (i) a \emph{finite-sample variance decomposition} that separates influence-function variance from remainder-induced variance and the covariance between them; (ii) a \emph{sandwich consistency theorem} that gives a precise necessary and sufficient condition -- strong remainder negligibility -- for the standard sandwich to be consistent for the total sampling variance, and shows this is strictly stronger than the product-rate condition that guarantees asymptotic linearity; (iii) two \emph{refined variance estimators} -- leave-one-unit-out jackknife and pairs cluster bootstrap -- each with full asymptotic validity guarantees in the near-boundary regime, together with a heteroskedasticity-corrected sandwich interpretation that is numerically equivalent to the jackknife Wald interval; and (iv) a \emph{clustered-data extension} in which the remainder interacts with intra-cluster correlation to produce an analytic formula for sandwich gap amplification.

翻译：在非参数模型中，渐近线性估计量通过冯·米塞斯展开实现其点估计保证，其中二阶余项被声明为可忽略。置信区间随后将一阶影响函数项视为抽样变异性的唯一来源。该推理在渐近意义下是精确的，但在有限样本中，只要二阶余项贡献的变异与影响函数方差同阶——我们称之为\emph{近边界区域}，其特征是干扰参数估计在乘积率阈值处或附近运行——该推理就可能实质性地失效。我们为此区域发展了一套通用的推断理论。我们的贡献包括：(i) 一个\emph{有限样本方差分解}，将影响函数方差与余项诱导的方差以及它们之间的协方差分离开来；(ii) 一个\emph{三明治一致性定理}，给出了标准三明治估计量对总抽样方差一致的一个精确充分必要条件——强余项可忽略性，并证明这严格强于保证渐近线性的乘积率条件；(iii) 两个\emph{精确方差估计量}——留一单位刀切法和成对聚类自助法——各自在近边界区域具有完全的渐近有效性保证，同时给出了一个异方差校正的三明治解释，其在数值上等价于刀切法Wald区间；以及(iv) 一个\emph{聚类数据扩展}，其中余项与簇内相关性相互作用，产生了三明治间隙放大的解析公式。