What is Doubly Robust Estimation?
Doubly Robust Estimation combines an outcome or reward model with an inverse-propensity correction so that, under the full identification conditions, the estimator can remain consistent when either the outcome model or propensity model is correctly specified.
Quick Facts
| Specification | Official Specification |
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How It Works
The correction targets outcome-model residuals
For a binary treatment ATE, AIPW starts with the modeled contrast m1(x) - m0(x) and adds inverse-propensity-weighted residuals for observed treated and control outcomes. For policy value, DR starts with the target policy's model-based value and corrects the logged action's residual by pi(a|x) / mu(a|x). This structure explains both its protection and its dependence on overlap.
Double robustness has precise boundaries
Bang and Robins formalize doubly robust missing-data and causal estimators: under the remaining assumptions, consistency can survive if either the outcome regression or assignment model is correct. It does not survive undefined treatments, interference, post-treatment adjustment, logging corruption, unsupported actions, or simultaneous misspecification of both nuisance models.
Cross-fit flexible nuisance models and preserve the inference unit
Training and scoring a high-capacity nuisance model on the same records can create overfit residuals and invalidate simple standard errors. Cross-fitting generates out-of-fold propensity and outcome predictions before computing the orthogonal score. Report overlap and weight diagnostics, compare the outcome-only, weighting-only, and DR estimates, and use cluster- or time-aware folds and uncertainty calculations when observations are dependent.
Key Characteristics
- Combines outcome regression with inverse-propensity correction
- Includes AIPW treatment-effect and DR policy-value estimators
- Can tolerate one correctly specified nuisance model under full assumptions
- Still requires consistency, overlap, and valid assignment assumptions
- Benefits from cross-fitting with flexible machine-learning nuisances
- Needs component estimates and uncertainty diagnostics for interpretation
Common Use Cases
- Estimating an average treatment effect from observational cohorts
- Evaluating recommendation policies from logged bandit feedback
- Auditing whether outcome-only and weighting-only estimates disagree
- Combining flexible reward models with randomized exploration logs
- Building orthogonal scores for semiparametric machine-learning pipelines
Example
Loading code...Frequently Asked Questions
Why is the estimator called Doubly Robust?
Under its identification and regularity conditions, it can remain consistent if either the outcome model is correct or the propensity model is correct. The phrase refers to these two nuisance-model routes; it does not mean the estimate is robust to every assumption failure.
What is the difference between AIPW and Doubly Robust policy evaluation?
AIPW commonly estimates treatment means or contrasts by augmenting inverse treatment weights with outcome regression. Contextual-policy DR uses the same principle with target-to-logging action ratios and a reward model. Their estimands and data structures differ even though the correction pattern is shared.
Does Doubly Robust Estimation remove the need for overlap?
No. The residual correction requires supported assignments or actions, and the outcome model must extrapolate where support is absent. Such extrapolation is an additional modeling assumption, not observed identification, so overlap violations must still be disclosed and bounded.
Why use cross-fitting with a Doubly Robust estimator?
Cross-fitting creates nuisance predictions for each record from models that did not train on that record. Combined with an orthogonal score, this reduces own-observation overfitting bias and permits flexible machine-learning nuisances under suitable rate and dependence conditions.
What should be reported with a Doubly Robust estimate?
Report the estimand, sample and assignment mechanism, overlap and weight diagnostics, nuisance-model training and cross-fitting scheme, outcome-only and weighting-only estimates, DR point estimate, uncertainty interval, slice sensitivity, and any clipping or trimming rule.