Unified treatment for jackknife designs with growing numbers of subsamples

Develop a unified treatment of jackknife inference for fixed effects models that accommodates designs with a growing number of subsamples (m → ∞), including delete-one/leave-one-out jackknife schemes, rather than restricting to fixed-m designs.

Background

The paper’s framework for jackknife inference is built around a fixed number m of subsample estimators, which enables simple constructions and accommodates dependence. However, this excludes classical delete-one/leave-one-out jackknife schemes and more general settings where the number of subsamples grows with sample size (m → ∞).

The authors explicitly note that they focus on fixed-m schemes and leave a unified treatment that includes m → ∞ designs to future work. Providing such a unified treatment would extend the applicability of their jackknife t-statistics and MVUJ estimators to widely used jackknife designs beyond fixed m.

References

By taking $m$ to be fixed in Assumption \ref{AJK} we rule out delete-one / leave-one-out jackknife schemes, and more generally designs with $m \to \infty$. We focus here on fixed $m$ schemes due to their computational simplicity and ability to accommodate dependence, leaving a unified treatment to future work.

— Jackknife Inference for Fixed Effects Models  (2602.21903 - Higgins, 25 Feb 2026) in Remark following Assumption AJK, Section 2 (Jackknife Inference)