# Cross-Fitting Under Nonregularity: Normality and Inference via Locality

arXiv: https://arxiv.org/abs/2610.02944 · HTML: https://mlsanity.com/paper/2610.02944/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 11 of 11)

- [Cross-validation Confidence Intervals for Test Error](https://mlsanity.com/paper/2007.12671/) (2020)
- [Evaluating Treatment Prioritization Rules via Rank-Weighted Average Treatment Effects](https://mlsanity.com/paper/2111.07966/) (2021)
- [Merging uncertainty sets via majority vote](https://mlsanity.com/paper/2401.09379/) (2024)
- [Significance tests of feature relevance for a black-box learner](https://mlsanity.com/paper/2103.04985/) (2021)
- [Cross-Validation with Confidence](https://mlsanity.com/paper/1703.07904/) (2017)
- [Decorrelated Variable Importance](https://mlsanity.com/paper/2111.10853/) (2021)
- [Fisher-Schultz Lecture: Generic Machine Learning Inference on Heterogenous Treatment Effects in Randomized Experiments, with an Application to Immunization in India](https://mlsanity.com/paper/1712.04802/) (2017)
- [The Limits of Assumption-free Tests for Algorithm Performance](https://mlsanity.com/paper/2402.07388/) (2024)
- [Inference on Optimal Policy Values and Other Irregular Functionals via Softmax Smoothing](https://mlsanity.com/paper/2507.11780/) (2025)
- [Training and Testing with Multiple Splits: A Central Limit Theorem for Split-Sample Estimators](https://mlsanity.com/paper/2511.04957/) (2025)
- [The Relative Instability of Model Comparison with Cross-validation](https://mlsanity.com/paper/2508.04409/) (2025)

## Abstract (arXiv)

Cross-fitting is routine in much of applied research. While conventional confidence intervals that ignore cross-fold dependence are asymptotically valid in several settings, they undercover in many applications that share a common form of nonregularity: from the classic cross-validation problem of testing whether a fitted model outperforms another, to testing for heterogeneous treatment effects with machine learning, to estimating the value of a potentially non-unique optimal treatment regime. Exploiting a new locality condition, I show that a large class of cross-fitting estimators still satisfies a central limit theorem despite the nonregularity, but with an asymptotic variance that must be adjusted for the cross-fold correlation. Then, I propose a method for estimating this correlation and construct new confidence intervals that attain asymptotically nominal coverage. Finally, I show that the proposed confidence intervals attain approximately nominal coverage in a simulation study with random forests and neural networks.