Connections between Survey Calibration Estimators and Semiparametric Models for Incomplete Data

Survey calibration (or generalized raking) estimators are a standard approach to the use of auxiliary information in survey sampling, improving on the simple Horvitz-Thompson estimator. In this paper we relate the survey calibration estimators to the semiparametric incomplete-data estimators of Robins and coworkers, and to adjustment for baseline variables in a randomized trial. The development based on calibration estimators explains the "estimated weights" paradox and provides useful heuristics for constructing practical estimators. We present some examples of using calibration to gain precision without making additional modelling assumptions in a variety of regression models.