Optimal calibration estimators in survey sampling
本文证明了模型校准估计量在有限总体均值估计中的最优性，并提出了分布函数、方差等参数的最优校准估计量，在模型误设下仍保持设计一致性，模拟显示改进显著。
We show that the model-calibration estimator for the finite population mean, which was proposed by Wu & Sitter (2001) through an intuitive argument, is optimal among a class of calibration estimators. We also present optimal calibration estimators for the finite population distribution function, the population variance, the variance of a linear estimator and other quadratic finite population functions under a unified framework. The proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified. A limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial. The question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology. Some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation. Copyright Biometrika Trust 2003, Oxford University Press.