Cross-Fitting Under Nonregularity: Normality and Inference via Locality
Abstract
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.
Related
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BibTeX
@misc{fava2026crossfitting,
title = {{Cross-Fitting Under Nonregularity: Normality and Inference via Locality}},
author = {Bruno Fava},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02944},
eprint = {2610.02944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02944},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cross-Fitting Under Nonregularity: Normality and Inference via Locality
AU - Bruno Fava
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02944
UR - https://arxiv.org/abs/2610.02944
AB - 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.
ER -