Rescuing double robustness: safe estimation under complete misspecification

Double robustness is a major selling point of semiparametric and missing data methodology. Its virtues lie in protection against partial nuisance misspecification and asymptotic semiparametric efficiency under correct nuisance specification. However, in many applications, complete nuisance misspecification should be regarded as the norm (or at the very least the expected default), and thus doubly robust estimators may behave fragilely. In fact, it has been amply verified empirically that these estimators can perform poorly when all nuisance functions are misspecified. Here, we first characterize this phenomenon of double fragility, and then propose a solution based on adaptive correction clipping (DR+ACC). We argue that our DR+ACC proposal is safe, in that it inherits the favorable properties of doubly robust estimators under correct nuisance specification, but its error is guaranteed to be bounded by a convex combination of the individual nuisance model errors, which prevents the instability caused by the compounding product of errors of doubly robust estimators. We also show that our proposal comes with no reduction in semiparametric efficiency compared to doubly robust estimators, and thus valid inference based on asymptotic normality can be conducted when nuisances are well-specified. We showcase the efficacy of our DR+ACC estimator both through extensive simulations and by applying it to the analysis of Alzheimer's disease proteomics data.