Multipurpose weighting for small area estimation

Sample surveys are generally multivariate, in the sense that they collect data on more than one response variable. In theory, each variable can then be assigned an optimal weight for estimation purposes. However, it is a distinct practical advantage to have a single weight for all variables collected in the survey. This article describes how such multipurpose sample weights can be constructed when small area estimates of the survey variables are required. The approach is based on the model-based direct (MBD) method of small area estimation described in Chandra and Chambers (2005). Empirical results reported in this article show that MBD estimators for small areas based on multipurpose weights perform well across a range of variables that are often of interest in business surveys. Furthermore, these results show that the proposed approach is robust to model misspecification when applied to variables (e.g., those that contain a significant proportion of zeros) that are not suited to linear model-based small area estimation methods.