### Abstract

When estimating the total of a variable in a finite population, the statistician is looking for some sampling strategy (sampling design , estimator) that may be considered as efficient in terms of its variance. The presentation is confined to the case of a study variable that is skewed to the right when, in addition, there is one quantitative auxiliary variable available.

Assuming that there is a super-population model that relates the study variable, y, to the auxiliary variable, x, and after some approximations, the strategy (πps, GREG estimator) minimizes the Anticipated Variance, and therefore is sometimes referred as optimal.

As the optimal strategy assumes that some characteristics of the model are completely known, it may be considered as strongly model-dependent. We compare its efficiency with the efficiency of some alternative strategies that may be considered less model-dependent. The alternative strategies are: (STSRS – HT estimator), (STSRS – GREG estimator), (STSRS – Poststratified estimator) and (πps – Poststratified estimator). The comparisons are made under different situations: when the model is well-specified and under different misspecifications of the model.