Unbiased estimation by calibration on distribution in simple sampling designs without replacement - ARCHIVED

The post-stratified estimator sometimes has empty strata. To address this problem, we construct a post-stratified estimator with post-strata sizes set in the sample. The post-strata sizes are then random in the population. The next step is to construct a smoothed estimator by calculating a moving average of the post-stratified estimators. Using this technique, it is possible to construct an exact theory of calibration on distribution. The estimator obtained is not only calibrated on distribution, it is also linear and completely unbiased. We then compare the calibrated estimator with the regression estimator. Lastly, we propose an approximate variance estimator that we validate using simulations.