INFERENCE FOR SEMIPARAMETRIC MODELS: SOME QUESTIONS AND AN ANSWER

By Peter J. Bickel, Jaimyoung Kwon. 2001

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Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, background): “Early contributions include Robins and Rotnitzky (2001), Van Der Laan and Dudoit (2003), and Rubin and van der Laan (2005).”
Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, background): “There exist diﬀerent approaches to this (Bickel and Kwon, 2001; Greenwood and Wefelmeyer, 1995).”
Comment: Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data. (2008, background): “1 nonrandom treatment assignment in observational studies and noncompliance in randomized experiments (Robins and Rotnitzky, 2001; van der Laan and Robins, 2003).”
Automated versus Do-It-Yourself Methods for Causal Inference: Lessons Learned from a Data Analysis Competition (2017, methodology): “While some approaches submitted fall either formally or informally under a “double robust” classification (Robins and Rotnitzky, 2001; van der Laan and Robins, 2003), we prefer to categorize methods separately by whether they model the assignment mechanism or the response surface since it is beyond…”
Comment: Performance of Double-Robust Estimators When “Inverse Probability” Weights Are Highly Variable (2007, methodology): “Robins and Rotnitzky (2001) described a general approach to the construction of DR estimators (when they exist) in a very large model class that includes all MAR and CAR models as well as certain nonignorable (i.e., non-CAR) missing data models.”
Causal Inference With General Treatment Regimes (2004, background): “For example, some authors suggest adjusting for the covariates in the within-subclass model (e.g., Robins and Rotnitzky 2001).”
Longitudinal Data Analysis. Handbooks of Modern Statistical Methods (2009, methodology): “Finally, Robins (2000) and Robins and Rotnitzky (2001) have also recently developed so-called “doubly robust” weighted estimators that relax the assumption that the model for the missingness probabilities, πi, has been correctly specified, albeit requiring additional assumptions on the model for Y…”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, background): “From (27) and (28), the second terms in (25) and (26) can be Op({log(p)/n}) in the supremum norms under sub-Gaussian errors.”
Unified Cross-Validation Methodology For Selection Among Estimators and a General Cross-Validated Adaptive Epsilon-Net Estimator: Finite Sample Oracle Inequalities and Examples (2003, unknown): “…we utilize inverse probability of censoring weighted and doubly robust locally efficient estimation methods for estimating this parameter based on the validation sample as presented in Robins and Rotnitzky (1992); Robins et al. (2000); Robins and Rotnitzky (2001); van der Laan and Robins (2002).”
Imputation Strategies for the Estimation of Natural Direct and Indirect Effects (2012, background): “Finally, the asserted property of double robustness may be somewhat illusory (Robins and Rotnitzky, 2001) because correct specification of the exposure and mediator model may anyway be essential in the face of incoherent model specification. Relative to our proposal, the approaches of van der Laan a”
A comparison of multiple imputation and doubly robust estimation for analyses with missing data (2006, background): “(1999) and in the contribution to the discussion of Bickel and Kwon (2001) by Robins and Rotnitzky) are robust under certain conditions to misspecification of the model for the probability of response. The pros and cons of this approach with respect to multiple imputation have been the subject of de”
Bias-Reduced Doubly Robust Estimation (2015, methodology): “Since the seminal work by Scharfstein, Rotnitzky, and Robins (1999a) and Robins and Rotnitzky (2001), a variety of DR estimators have been developed.”
The International Journal of Biostatistics (2017, unknown): “In particular, double robust locally eﬃcient augmented IPCW-estimators have been developed (Robins and Rotnitzky (2001b), Robins and Rotnitzky (2001a), Robins et al. (2000b), Robins (2000a), van der Laan and Robins (2003), Neugebauer and van der Laan (2005), Yu and van der Laan (2003)).”
Structural nested models and G-estimation: the partially realized promise (2014, methodology): “…α and γ are variation-independent, then socalled G-estimators that solve (33) and (34), obtained upon substituting α∗ and γ∗ by consistent estimators, are doubly robust (Robins and Rotnitzky, 2001): consistent when the SNM and either model A or model B is correctly specified, regardless of which.”