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Calibration estimators and semiparametric models

Survey calibration estimators were developed at the same time as the AIPW estimators for incomplete data models of Robins & Rotnitzky and coworkers. They turn out to be closely related, but much easier to understand. I will describe the construction of calibration estimators and how they solve the `estimated weights` paradox. I will give some examples of the use of calibration estimators. Calibration and AIPW estimators are not fully efficient when a semiparametric model for the complete data is known, but I will examine how this efficiency comparison holds up when the semiparametric model is only nearly true.