In the sample survey randomization model, characterizations are given of those functions of the parameter which are estimable, those which have an admissible estimator, and those which have a uniform minimum variance unbiased estimator. These characterizations are effected via an explicit canonical decomposition of the relevant parametric functions. This decomposition leads to a natural generalization of the classical Horvitz-Thompson estimator, and seems to be of some combinatorial interest. In Part II, classical results about population totals are extended to arbitrary parametric functions, emphasizing optimal properties and characterizations of generalized Horvitz-Thompson estimators. 1
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