A "Super-Population Viewpoint" for Finite Population Sampling

Frequently it is reasonable for a sample surveyor to view the finite population of interest as an independent sample of size N from an infinite super-population. This super-population viewpoint is contrasted to the classical frequentist theory of finite population sampling and the classical theory of infinite population sampling. A new technique for making inferences about finite population "parameters' is developed and shown to be applicable for any survey design. Two example applications are given: the estimation of strata- and population means in stratified sampling and the use of the so-called regression estimators for the same purpose.