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We consider estimation of average treatment effects given observational datawith high-dimensional pretreatment variables. Existing methods for this problemtypically assume some form of sparsity for the regression functions. In thiswork, we introduce a debiased inverse propensity score weighting (DIPW) schemefor average treatment effect estimation that delivers $\sqrt{n}$-consistentestimates when the propensity score follows a sparse logistic regression model;the outcome regression functions are permitted to be arbitrarily complex. Wefurther demonstrate how confidence intervals centred on our estimates may beconstructed. Our theoretical results quantify the price to pay for permittingthe regression functions to be unestimable, which shows up as an inflation ofthe variance of the estimator compared to the semiparametric efficient varianceby a constant factor, under mild conditions. We also show that when outcomeregressions can be estimated faster than a slow $1/\sqrt{ \log n}$ rate, ourestimator achieves semiparametric efficiency. As our results accommodatearbitrary outcome regression functions, averages of transformed responses undereach treatment may also be estimated at the $\sqrt{n}$ rate. Thus, for example,the variances of the potential outcomes may be estimated. We discuss extensionsto estimating linear projections of the heterogeneous treatment effect functionand explain how propensity score models with more general link functions may behandled within our framework. An R package \texttt{dipw} implementing ourmethodology is available on CRAN.

Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders