A Debiased Machine Learning Single-Imputation Framework for Item Nonresponse in Surveys

Abstract

Machine-learning methods offer flexible alternatives to parametric models for imputing missing survey values. However, using their predictions in the customary imputed estimator does not automatically yield valid inference. We explain why the error from estimating the regression function can prevent root-$n$ consistency and develop inference for a finite population mean using a cross-fitted augmented inverse-probability-weighted (AIPW) estimator. The analysis combines an imputation model, a sampling design, and a missing-at-random response mechanism, while allowing dependence among sampling indicators. We establish double robustness and show that, under suitable regularity conditions, consistency of both nuisance estimators together with a product-rate condition yields oracle equivalence and asymptotic normality. We also derive consistent variance estimators accounting for sampling and nonresponse. To obtain a completed survey variable, we construct adjusted imputed values that preserve observed responses and whose weighted mean reproduces the AIPW estimate exactly. We further discuss aggregation of nuisance learners and the conditions under which it preserves the prediction rates needed for inference. Simulations show that cross-fitting can substantially reduce undercoverage, but may increase mean squared error when nuisance predictions are inaccurate.