An optimal calibration distance leading to the optimal regression estimator - ARCHIVED

When there is auxiliary information in survey sampling, the design based "optimal (regression) estimator" of a finite population total/mean is known to be (at least asymptotically) more efficient than the corresponding GREG estimator. We will illustrate this by some simulations with stratified sampling from skewed populations. The GREG estimator was originally constructed using an assisting linear superpopulation model. It may also be seen as a calibration estimator; i.e., as a weighted linear estimator, where the weights obey the calibration equation and, with that restriction, are as close as possible to the original "Horvitz-Thompson weights" (according to a suitable distance). We show that the optimal estimator can also be seen as a calibration estimator in this respect, with a quadratic distance measure closely related to the one generating the GREG estimator. Simple examples will also be given, revealing that this new measure is not always easily obtained.