Connections between survey calibration estimators and semiparametric models for incomplete data

Area of Science:

• Statistics
• Survey Methodology
• Data Analysis

Background:

• Survey calibration (generalized raking) is a standard method for incorporating auxiliary information in survey sampling.
• It offers improvements over the basic Horvitz-Thompson estimator.
• Understanding its relationship with other statistical techniques can enhance its application.

Purpose of the Study:

• To connect survey calibration estimators with semiparametric incomplete-data estimators and baseline variable adjustment in randomized trials.
• To explain the 'estimated weights' paradox within the framework of calibration estimators.
• To provide practical heuristics for constructing effective survey estimators.

Main Methods:

• Relating survey calibration estimators to Robins and coworkers' semiparametric incomplete-data estimators.
• Connecting calibration estimators to adjustment for baseline variables in randomized trials.
• Developing a framework based on calibration estimators to explain the 'estimated weights' paradox.

Main Results:

• Established a link between survey calibration estimators and semiparametric incomplete-data estimators.
• Provided a theoretical explanation for the 'estimated weights' paradox.
• Demonstrated how calibration can enhance precision in various regression models without additional assumptions.
• Offered practical heuristics for constructing improved survey estimators.

Conclusions:

• Survey calibration estimators offer a robust framework for integrating auxiliary information.
• The connection to other methods clarifies theoretical aspects and practical applications.
• Calibration provides a valuable tool for improving survey precision efficiently.