Advances in Business Statistics, Methods and Data Collection

30Bayesian Methods Applied to Small Area Estimation for Establishment Statistics

Paul A. Parker¹, Ryan Janicki², and Scott H. Holan^1,3

¹Department of Statistics, University of Missouri, Columbia, MO, USA

²Center for Statistical Research and Methodology, U.S. Census Bureau, Washington, DC, USA

³Office of the Associate Director for Research and Methodology, U.S. Census Bureau, Washington, DC, USA

30.1 Introduction

Much of the literature on small area estimation (SAE) has been focused on analysis of data collected from household surveys or surveys of individuals. In principle, many of the same methods used to analyze household or individual survey data can be applied to the analysis of establishment‐level survey data, although there are some fundamental differences in the characteristics of the data, as well as the survey design used to collect the data (Burgard et al., 2014). In establishment surveys, stratified sampling designs are typically used, where the strata are determined using cross classifications of business registry variables, such as employment size variables and industry classifications, as well as geographic variables (Hidiroglou and Lavallée, 2009). These stratified sampling designs, which are stratified with respect to industry and/or business size class, result in highly variable selection probabilities and sampling weights (Zimmerman and Münnich, 2018). The size variables that are used to stratify the population in establishment surveys are typically correlated ...