Understanding calibration estimators in survey sampling - ARCHIVED

There exist well known methods due to Deville and Sárndal (1992) which adjust sampling weights to meet benchmark constraints and range restrictions. The resulting estimators are known as calibration estimators. There also exists an earlier, but perhaps not as well known, method due to Huang and Fuller (1978). In addition, alternative methods were developed by Singh (1993), who showed that similar to the result of Deville-Sárndal, all these methods are asymptotically equivalent to the regression method. The purpose of this paper is threefold: (i) to attempt to provide a simple heuristic justification of all calibration estimators (including both well known and not so well known) by taking a non-traditional approach; to do this, a model (instead of the distance function) for the weight adjustment factor is first chosen and then a suitable method of model fitting is shown to correspond to the distance minimization solution, (ii) to provide to practitioner computational algorithms as a quick reference, and (iii) to illustrate how various methods might compare in terms of distribution of weight adjustment factors, point estimates, estimated precision, and computational burden by giving numerical examples based on a real data set. Some interesting observations can be made by means of a descriptive analysis of numerical results which indicate that while all the calibration methods seem to behave similarly to the regression method for loose bounds, they however seem to behave differently for tight bounds.