Using auxiliary information under a generic sampling design

Under a generic sampling design we consider a class of asymptoticallyunbiased estimators for the mean of a nite population when auxiliary informationis available. After obtaining the minimum variance bound of the class we nd thatthe regression estimator is the best one to use and that recent estimators proposedby Bacanli and Kadilar (2008) are unsatisfactory solutions. Finally, we carry outa simulation study under unequal probability sampling - with estimated rst andsecond order inclusion probabilities - to shed light on the performance of dierentestimators.