Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders
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We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers √(n)-consistent estimates of the average treatment effect when the propensity score follows a sparse logistic regression model; the regression functions are permitted to be arbitrarily complex. Our theoretical results quantify the price to pay for permitting the regression functions to be unestimable, which shows up as an inflation of the variance of the estimator compared to the semiparametric efficient variance by at most O(1) under mild conditions. Given the lack of assumptions on the regression functions, averages of transformed responses under each treatment may also be estimated at the √(n) rate, and so for example, the variances of the potential outcomes may be estimated. We show how confidence intervals centred on our estimates may be constructed, and also discuss an extension of the method to estimating projections of the heterogeneous treatment effect function.
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