Title: A new central limit theorem for the augmented IPW estimator: variance inflation, cross-fit covariance and beyond
Authors: Rajarshi Mukherjee - Harvard T.H. Chan School of Public Health (United States) [presenting]
Kuanhao Jiang - Harvard University (United States)
Subhabrata Sen - Harvard University (United States)
Pragya Sur - Harvard University (United States)
Abstract: In recent times, inference for the ATE in the presence of high-dimensional covariates has been extensively studied. Among the diverse approaches that have been proposed, augmented inverse propensity weighting (AIPW) with cross-fitting has emerged as a popular choice in practice. We study this cross-fit AIPW estimator under well-specified outcome regression and propensity score models in a high-dimensional regime where the number of features and samples are both large and comparable. Under assumptions on the covariate distribution, we establish a new CLT for the suitably scaled cross-fit AIPW that applies without any sparsity assumptions on the underlying high-dimensional parameters. Our CLT uncovers two crucial phenomena among others: (i) the AIPW exhibits substantial variance inflation that can be precisely quantified in terms of the signal-to-noise ratio and other problem parameters, (ii) the asymptotic covariance between the pre-cross-fit estimates is non-negligible even on the root-n scale. Finally, we complement our theoretical results with simulations that demonstrate both the finite sample efficacy of our CLT and its robustness to our assumptions.