AI 中文总结
研究针对半参数推断开发V折刀切法，它计算高效且理论合理，仅需V次留一法重拟合，利用伪值经验离散度量化不确定性，给出有效置信区间和同时置信带，扩展理论到特定估计量，模拟证实其可靠推断。
AI 中文摘要
几十年来，自助法一直是统计推断的默认工具，因其适用性广且分析要求低。虽然其对光滑参数估计量的有效性已为人熟知，但对许多现代半参数和机器学习估计量的理论性质仍研究不足。我们开发了V折刀切法作为半参数推断的一种计算高效且理论合理的替代方法。它仅需V次留一法重拟合，并利用刀切法伪值的经验离散度来量化不确定性，无需推导或评估影响函数。对于路径可微参数的正则渐近线性估计量，我们表明，对于固定的V，学生化V折刀切法统计量收敛到自由度为V - 1的t分布，即使刀切方差估计量不依概率收敛也能给出有效的置信区间。当V趋于无穷时，我们建立了方差估计量以V的负二分之一次方速率的一致性，允许V缓慢发散，例如以对数n的速率。我们还基于正确的分量学生化极限分布开发了同时置信带。最后，我们将理论扩展到具有发散影响函数方差和慢于根号n收敛速度的广义渐近线性估计量；学生化的尺度不变性消除了知道有效收敛速度的必要性。对平均治疗效果、Kaplan - Meier生存曲线和高度自适应lasso剂量反应曲线的模拟证实了可靠的推断，包括基于影响函数的标准误差是反保守或不稳定的情况。
英文摘要
For decades, the bootstrap has been a default tool for statistical inference because of its broad applicability and minimal analytic requirements. Although its validity is well understood for smooth parametric estimators, its theoretical properties for many modern semiparametric and machine-learning estimators remain largely unstudied. Nevertheless, bootstrap procedures are often used routinely in such settings, even when their validity is unknown and their computational cost is substantial. We develop the $V$-fold jackknife as a computationally efficient and theoretically justified alternative for semiparametric inference. It requires only $V$ leave-fold-out refits and uses the empirical dispersion of jackknife pseudo-values to quantify uncertainty, without deriving or evaluating an influence function. For regular asymptotically linear estimators of pathwise differentiable parameters, we show that, for fixed $V$, the Studentized $V$-fold jackknife statistic converges to a $t$-distribution with $V-1$ degrees of freedom, giving valid confidence intervals even though the jackknife variance estimator does not converge in probability. When $V\to\infty$, we establish consistency of the variance estimator at rate $V^{-1/2}$, allowing $V$ to diverge slowly, for example at rate $\log n$. We also develop simultaneous confidence bands based on the correct componentwise-Studentized limiting distribution. Finally, we extend the theory to generalized asymptotically linear estimators with diverging influence-function variance and slower-than-$\sqrt n$ convergence; scale invariance of Studentization eliminates the need to know the effective convergence rate. Simulations on the average treatment effect, Kaplan--Meier survival curve, and highly adaptive lasso dose-response curves confirm reliable inference, including where influence-function-based standard errors are anti-conservative or unstable.
