Debiased Calibration Estimation Using Generalized Entropy in Survey Sampling

Incorporating auxiliary information into the survey estimation is a fundamental problem in survey sampling. Calibration weighting is a widely used technique to integrate such information by adjusting design weights to meet benchmarking constraints. Traditional methods, such as those proposed by <i>Deville and Särndal</i>, solve this problem by minimizing a distance between calibrated and design weights. In this article, we propose a novel calibration framework that instead maximizes a generalized entropy function subject to two constraints: a benchmarking constraint to improve efficiency and a debiasing constraint involving design weights to ensure design consistency. This approach avoids placing design weights in the objective function and instead incorporates them through the constraint structure. We establish the asymptotic properties of the proposed estimator, including design consistency and asymptotic normality, and demonstrate that under Poisson sampling, a specific contrast-entropy function minimizes the asymptotic variance among a broad class of entropy functions. Simulation studies and an empirical application to agricultural survey data illustrate the advantages of our method, particularly in the presence of model misspecification or informative sampling designs. We demonstrate a real-life application using agricultural survey data collected from Kynetec, Inc. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.