A STABLE AND MORE EFFICIENT DOUBLY ROBUST ESTIMATOR

Under the assumption of missing at random, doubly robust (DR) estimators are consistent when either the propensity score or the outcome model is correctly specified. However, despite its appealing theoretic properties, it has been show that the usual augmented inverse probability weighted (IPW) DR estimator may exhibit unsatisfying behavior. We propose an alternative DR method for mean estimation. In this method, we do not directly weight outcomes by the inverse of the estimated propensity scores. Instead we use a nonparametric kernel regression to model the residuals from an outcome regression model as a function of propensity scores. The proposed method does not suffer from the instability of the usual IPW estimator in the event of small estimated propensities. We show that, asymptotically, the new estimator has the double robustness property. Moreover, we show that it is guaranteed to be more efficient than the usual augmented IPW DR estimator when the propensity score model is correct, but the outcome model is incorrect. Our simulation studies show that its finite-sample performance improves upon that of existing DR estimators.