Multipurpose small area estimation

Abstract

Sample surveys are generally multivariate, in the sense that they measure more than one
response variable. In theory, each variable can then be assigned an optimal weight for
estimation purposes. However, it is often a distinct practical advantage to have a single
weight that is used with all variables collected in the survey. This paper 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 Chambers and Chandra (2006). Empirical
results reported in this paper 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 and also efficient for the variables ill-suited to standard methods
of small area estimation (e.g. variables that contain a significant proportion of zeros).

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