Bias-Reduced Doubly Robust Estimation

These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root- n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model.

In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estimator under misspecification of both working models and results in doubly robust estimators with easy-to-calculate asymptotic variance.