Rescuing double robustness: safe estimation under complete misspecification

2025-09-26

AI Summary

This paper identifies a “double fragility” phenomenon in doubly robust (DR) estimators: their performance deteriorates sharply when both nuisance models are simultaneously misspecified, undermining their practical robustness. To address this, we propose a safe estimation framework featuring an adaptive calibrated truncation (ACC) mechanism, which ensures that the estimation error is governed by a convex combination of the individual nuisance model errors—thereby preventing error accumulation. We provide the first theoretical characterization of double fragility and prove that the proposed estimator achieves semiparametric efficiency under correct model specification, while retaining consistency and stability even under complete misspecification of both nuisance models. By integrating semiparametric inference with parametric bootstrap, the method exhibits strong robustness in high-dimensional settings. Simulation studies and analysis of Alzheimer’s disease proteomics data demonstrate substantial improvements over conventional DR estimators, offering both rigorous theoretical guarantees and empirical effectiveness.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 (ACC). We argue that our 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 provides valid inference through the parametric bootstrap when nuisances are well-specified. We showcase the efficacy of our ACC estimator both through extensive simulations and by applying it to the analysis of Alzheimer's disease proteomics data.

Problem

• Addresses fragility of doubly robust estimators under complete nuisance misspecification
• Proposes adaptive correction clipping to bound estimation error safely
• Ensures valid inference while maintaining efficiency under correct specification

Innovation

• Adaptive correction clipping prevents error compounding
• Bounded error by convex combination of nuisance errors
• Valid inference via parametric bootstrap for well-specified nuisances