When Sample-Splitting Choices Matter in TMLE and AIPW: Cross-Fitting, Targeting, and Repetition

Abstract

Variants of targeted maximum likelihood estimation (TMLE) and augmented inverse-probability weighting (AIPW) with machine-learning nuisance models differ in which observations train them, how bias is corrected, and whether splits are repeated. In known-truth simulations of a binary-outcome average treatment effect, eight headline estimators shared each setting's library, inner folds and truncation bound; coverage differences were judged against a prespecified two-percentage-point margin. With a low-complexity library and good overlap (n = 3000), all but a half-sample baseline covered equivalently (0.928-0.939). With one random forest on the primary data-generating mechanism, estimators fitting the propensity in-sample undercovered severely (0.12-0.48), whereas cross-fitting both nuisances raised coverage to 0.91-1.00, two overcovering. Under near-positivity, every AIPW estimator covered better than every TMLE estimator with the unweighted fluctuation (0.907-0.917 versus 0.656-0.806 at the primary setting, all undercovering); looser truncation widened the gap. At the primary settings, pooled-versus-fold-specific and single-versus-double cross-fit constructions (involving four additional estimators) were usually equivalent; under extreme weights, pooled-targeting estimates were 1.7-1.8 times as dispersed as fold-specific ones. Repetition reduced partition dependence but made several intervals more conservative. Two real-data analyses illustrate these sensitivities. Results support cross-fitting both nuisances when empirical-process conditions cannot be justified, and assessing truncation and AIPW-versus-TMLE sensitivity under poor overlap.