ABSTRACT
Writing a finite population total Y as Y = iYi = sYi + r Yi an estimator t = t(s, Y ) for it may be written as t = sYi + (t − sYi), where s(r ) is the sum over the distinct units sampled (unsampled). Here a sample s is supposed to be chosen yielding the survey data d = (i, Yi|i ∈ s). To find a value t(d ) close to Y is equivalent to deriving from Yi, i ∈ s a quantity, t(d ) − sYi, which is close to r Yi. In order to achieve this we need a link between Yi, i /∈ s and Yi, i ∈ s. So far, a link established by a design p has been exploited. Even where a superpopulation model entered the scene, we did not use it to bridge the “gap” between Yi, i ∈ s and Yi, i /∈ s. We only took advantage of the model when deciding for a specific strategy ( p, t) and then based our conclusions on p alone.
