Statistical inference from finite population samples: A critical review of frequentist and Bayesian approaches

In survey sampling, data are obtained on a subset of a finite population by probability or nonprobability sampling procedures. These data are used to compute point estimates of finite population parameters along with their associated variance estimates and confidence intervals. Methods to conduct inferences and evaluate the properties of sampling and estimation procedures have been the subject of discussion and debate in the second half of the 20th century. In this article, we propose a critical review of three inferential approaches in a finite population context: the design-based approach, the frequentist model-based approach, and the Bayesian approach.