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arXiv

Cross-fitting still satisfies a central limit theorem under nonregularity, but its variance must be adjusted for cross-fold correlation

For a common form of nonregularity in cross-fitting (testing whether a fitted model outperforms another, testing heterogeneous treatment effects with machine learning, and estimating the value of a potentially non-unique optimal treatment regime), the paper introduces a new locality condition and shows that a large class of cross-fitting estimators still satisfies a central limit theorem, but with an asymptotic variance that must be adjusted for cross-fold correlation; the author proposes a method to estimate this correlation and constructs new confidence intervals that attain asymptotically nominal coverage, with a simulation study using random forests and neural networks showing approximately nominal coverage.