An Old Approach to Finite Population Sampling Theory
Richard M. Royall · Journal of the American Statistical Association · 1968
The main objective of this work is to relate classical inference and sampling theory (and current sampling practice) to recent advances toward formalizing and unifying the theory of sampling from finite populations. It is pointed out that the use of definitions which coincide with what seem to be the traditional notions of simple random sampling, and post-stratification (stratification after sampling) leads to the solution of such riddles which appear in the more recent theory as the failure of the likelihood principle to sanction any non-trivial inference whatever. In particular, a general method of maximum likelihood is shown to lead to new estimates for the population mean when the three aforementioned sampling plans are employed. Thus objective likelihood inference from sample to population is seen in these instances to be possible if and only if randomization is employed in the selection of the sample. Finally, completeness theorems are proved which imply that in the simplest common sampling problems conventional unbiased estimators of population parameters have the happy property of being the unique unbiased estimators.