Comment: Performance of Double-Robust Estimators When ``Inverse Probability'' Weights Are Highly Variable

Abstract

We thank the editor Ed George for the opportunity to discuss the paper by Kang and Schaeffer. The authors’ paper provides a review of doublerobust (equivalently, double-protected) estimators of (i) the mean μ = E(Y ) of a response Y when Y is missing at random (MAR) (but not completely at random) and of (ii) the average treatment effect in an observational study under the assumption of strong ignorability. In our discussion we will depart from the notation in Kang and Schaeffer (throughout, K&S) and use capital letters to denote random variables and lowercase letter to denote their possible values. In the missing-data setting (i), one observes n i.i.d. copies of O = (T,X,TY ), where X is a vector of always observed covariates and T is the indicator that the response Y is observed. An estimator of μ is double-robust (throughout, DR) if it remains consistent and asymptotically normal (throughout, CAN) when either (but not necessarily both) a model for the propensity score π(X) ≡ P (T = 1|X) = P (T = 1|X,Y ) or a model for the conditional mean m(X)≡

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@inproceedings{Robins2008CommentPO, title={Comment: Performance of Double-Robust Estimators When ``Inverse Probability'' Weights Are Highly Variable}, author={James M. Robins and Mariela Sued and Quanhong Lei-Gomez and Andrea Rotnitzky}, year={2008} }