Inferential Issues in Model-based Small Area Estimation: Some History and Selective Recent Advances

Abstract

Model-based Small Area Estimation (SAE) has seen rapid growth over the past 25 years or so due to the rapidly increasing demand for reliable small area estimators of totals, means and more complex area parameters. Direct area-specific estimators are either unreliable (due to small area-specific sample sizes) or not feasible (due to zero area-specific sample sizes). It is therefore necessary to borrow strength from related areas through implicit or explicit models linking related areas. We focus on explicit area-level and unit-level models. After a brief historical sketch of the evolution of SAE, we focus on selective recent developments (mostly after 2015). Developments before 2015 are mostly covered in the comprehensive Wiley book by Rao and Molina (2015). Under a basic area-level model, we consider semi-parametric and robust estimation of small area means under model misspecifications. Under a basic unit level model, methods for estimating complex parameters, such as poverty indicators, will be presented, including robust estimation in the presence of outliers. A comparison of area-level and unit-level models when unit level data are available will also be presented. Estimation methods studied include empirical best linear unbiased prediction (EBLUP), empirical best (EB) and hierarchical Bayes (HB).