# Jackknife Variance Estimation for H'ajek-Dominated Generalized U-Statistics

arXiv: https://arxiv.org/abs/2509.12356 · HTML: https://mlsanity.com/paper/2509.12356/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [Asymptotic Distributions and Rates of Convergence for Random Forests via Generalized U-statistics](https://mlsanity.com/paper/1905.10651/) (2019)
- [Randomized incomplete U-statistics in high dimensions](https://mlsanity.com/paper/1712.00771/) (2017)
- [Approximating high-dimensional infinite-order U-statistics: statistical and computational guarantees](https://mlsanity.com/paper/1901.01163/) (2019)
- [On Variance Estimation of Random Forests with Infinite-Order U-statistics](https://mlsanity.com/paper/2202.09008/) (2022)
- [Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors](https://mlsanity.com/paper/1808.08469/) (2018)

## Built on by (most cited first, 1 of 1)

- [Empirical Likelihood for Random Forests and Ensembles](https://mlsanity.com/paper/2511.13934/) (2025)

## Abstract (arXiv)

Valid uncertainty quantification for subsampling-based and randomized estimators often depends on variance estimators whose behavior is much less understood than that of the underlying point estimator. We prove ratio-consistency of the jackknife variance estimator, and certain delete-d variants, for a broad class of generalized U-statistics whose variance is asymptotically dominated by their Hajek projection and whose normalized first-projection squares satisfy a row-wise Lr weak law, with the classical fixed-order case recovered as a special instance. This projection-dominance plus square-LLN structure unifies and generalizes several criteria from the existing literature, clarifies when the simple nonparametric jackknife is theoretically justified in the generalized setting, and yields consistent variance estimation for the two-scale distributional nearest-neighbor regression estimator under substantially weaker conditions than previously required.