Forgot the sampling scheme at the estimation stage? - ARCHIVED

For a class of linear unbiased estimators in a class of sampling schemes, it is shown that one can forget the weights used for sample selection while estimating a population ratio by a ratio of two unbiased estimators, respectively of the numerator and the denominator defining the population ratio. This class of schemes includes commonly used sampling schemes such as unequal probability sampling with or without replacement, stratified proportional allocation sampling with unequal selection probabilities and without replacement in each stratum, etc.