The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands

2026-07-27 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning, Health & Medical Research · Depth: Expert, extended

Summary

The V-fold jackknife is introduced as a computationally efficient and theoretically justified alternative to the bootstrap for semiparametric inference, particularly for modern machine-learning estimators where bootstrap validity is often unstudied or computationally costly. This procedure requires only V leave-fold-out refits, using the empirical dispersion of jackknife pseudo-values to quantify uncertainty without requiring analytic influence function derivation. For regular asymptotically linear estimators, the Studentized V-fold jackknife statistic converges to a t-distribution with V-1 degrees of freedom for fixed V, providing valid confidence intervals. When V diverges, consistency of the jackknife variance estimator is established at rate V^-1/2, allowing V to grow slowly (e.g., log n). The method also supports simultaneous confidence bands and extends to generalized asymptotically linear estimators with slower-than-sqrt(n) convergence, demonstrating scale invariance. Simulations confirm reliable inference for average treatment effect, Kaplan–Meier survival curves, and highly adaptive lasso dose-response curves, even where influence-function-based standard errors are anti-conservative or unstable.

Key takeaway

For Research Scientists or Data Scientists developing or applying semiparametric and machine learning estimators, you should consider the V-fold jackknife as a robust alternative to the bootstrap. It offers strong theoretical guarantees and computational efficiency, especially when bootstrap validity is uncertain or refitting costs are high. You can achieve reliable coverage with as few as V=5 folds, accepting wider intervals for increased robustness, or increase V for narrower intervals as sample size grows. This method simplifies variance estimation for complex models, including those with non-standard convergence rates.

Key insights

The V-fold jackknife offers a computationally efficient and theoretically sound alternative for semiparametric inference.

Principles

• Fixed V (>=2) yields valid t-distribution inference.
• Studentization with t_V-1 corrects for finite degrees of freedom.
• Scale invariance adapts to unknown convergence rates.

Method

The procedure involves V leave-fold-out refits, evaluating the estimator on subsamples and basing inference on the dispersion of fold-level pseudo-values, avoiding analytic influence function derivation.

In practice

• Apply to average treatment effect, Kaplan–Meier survival, and HAL dose-response.
• Use t_V-1 critical values for robust confidence intervals.
• Simulate critical values for simultaneous confidence bands.

Topics

• V-fold Jackknife
• Semiparametric Inference
• Variance Estimation
• Confidence Intervals
• Bootstrap Methods
• Machine Learning Estimators
• Targeted Minimum Loss-based Estimation

Best for: AI Scientist, Data Scientist, Research Scientist

Related on AIssential

• Jackknife+ — the 2021 breakthrough you probably don’t use — Jackknife+ provides distribution-free prediction intervals for complex machine learning models.
• Kernel Ridge Regression Inference — New uniform confidence bands for Kernel Ridge Regression enable robust inference on nonstandard data types.
• Data augmented bootstrap: Unifying confidence interval construction by approximate invariance — DAB unifies confidence interval construction by leveraging approximate data invariances, bridging classical and modern statistical methods.
• Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimiser — VMPO minimizes log importance weight variance for diffusion alignment, unifying existing methods and suggesting new designs.
• tsbootstrap: Distribution-Free Uncertainty Quantification and Conformal Prediction for Time Series — tsbootstrap unifies advanced resampling and conformal prediction to provide robust, distribution-free uncertainty quantification for time series.
• Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies — A new differentially private bootstrap method enables robust statistical inference with strong privacy guarantees.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.