  We establish a mathematical framework that formally validates the two-phase
``super-population viewpoint'' proposed by Hartley and Sielken [Biometrics 31
(1975) 411--422] by defining a product probability space which includes both
the design space and the model space. The methodology we develop combines
finite population sampling theory and the classical theory of infinite
population sampling to account for the underlying processes that produce the
data under a unified approach. Our key results are the following: first, if the
sample estimators converge in the design law and the model statistics converge
in the model, then, under certain conditions, they are asymptotically
independent, and they converge jointly in the product space; second, the sample
estimating equation estimator is asymptotically normal around a
super-population parameter.
