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：半参数模型中的渐近线性估计量通过冯·米塞斯展开实现点估计保证，其中二阶余项被假定为可忽略。置信区间进而将一阶影响函数项视为抽样变异性的唯一来源。此推理在渐近意义下精确，但在有限样本中可能显著失效——当二阶余项贡献的变异性与影响函数方差同阶时，我们称之为**近边界区间**，其特征是干扰项估计在乘积率阈值附近或达到该阈值运行。我们为该区间建立了通用推断理论，主要贡献包括：(i) **有限样本方差分解**，将影响函数方差、余项诱导方差及其协方差分离；(ii) **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性的精确充要条件——即强余项可忽略性，并证明该条件严格强于保证渐近线性的乘积率条件；(iii) **两种精细化方差估计量**——逐单元留一法刀切法与配对簇自助法，在近边界区间内均具有完全渐近有效性保证，同时给出与刀切沃尔德区间数值等价的异方差校正三明治解释；(iv) **聚类数据扩展**，揭示余项与簇内相关性的交互作用，推导出三明治间隙放大的解析公式。