Sampling Variance Estimation Methods in Area Level of Small Area Estimation: A Narrative Review

Abstract

Introduction: In area level small area estimation (SAE) (Fay–Herriot and extension of it in spatial structure) sampling variances are assumed to be known. That is a powerful assumption and may be quite restrictive in some applications. The main in this field is the estimation of sampling variances for the small area parameters, which is necessary for obtaining reliable estimates and for evaluating the precision of the estimates.

Methods: The main objective of this article is to review some of the commonly used sampling variance estimation methods in area level of SAE. Information used to write this paper was collected from the sources of Google scholar, Scopus, MEDLINE and Web of Science and Hand searches of the references of retrieved literature.

Results: In the context of small area estimation, sampling variance estimation methods at the area level can be broadly classified into six ctegories: Direct Sampling Variance Estimator, Design-Based Variance Estimator, Generalized Variance Function, Model-based, Empirical Bayes and Extended methods.

Conclusion: According to the reviewed studies, no method can be reported as the best method for estimating the sampling variance in all conditions. Because each method needs different information, and on the other hand, simulation studies are needed to compare the methods.