Optimal calibration estimators in survey sampling

According to recent literature, the calibration method has gained much popularity on survey sampling and calibration estimators are routinely computed by many survey organizations. The choice of calibration variables for all existing approaches, however, remains ad hoc. In this article, we show that the model-calibration estimator for the finite population mean, which was proposed by Wu and Sitter (2001) through an intuitive argument, is indeed optimal among a class of calibration estimators. We further present optimal calibration estimators for the finite population distribution function, the population variance, variance of a linear estimator and other quadratic finite population functions under a unified framework. 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 generalized regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology. Constructions of proposed estimators under two-phase sampling and some fundamental issues in using auxiliary information from survey data are also addressed under the context of optimal estimation.