The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands
半参数推断的 V 折刀切法：方差、置信区间与同时置信带AI 解读 ↓
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半参数推断的 V 折刀切法：方差、置信区间与同时置信带
- 研究问题
- 对半参数及机器学习估计量，能否仅用少量留折重拟合获得可靠区间与置信带，并避免显式计算影响函数？
- 方法与思路
- 作者利用 V 次留折重拟合生成伪值，以其离散程度量化不确定性，分别研究固定折数、增长折数与较慢收敛情形。
- 材料陈述的贡献
- 摘要称固定 V 的学生化统计量趋于自由度 V−1 的 t 分布，增长 V 时方差估计一致，并扩展至同时置信带。
- 阅读关注点
- 应核对渐近线性与路径可微条件、留折估计的联合极限，以及固定折数方差不一致时区间为何仍有效。
- 阅读边界
- 这是预印本，同行评审与期刊接收均未核实。结果针对摘要所述估计量类别，不能据此认定任意机器学习估计均适用。
原文摘要
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.