Measurement error in small area estimation: a literature review

Abstract

Recent development in small area estimation has been related to the measurement errors in the auxiliary variables. The development has been driven by the fact that in standard small area estimation the auxiliary variables in the model are assumed to be measured without error. This type of auxiliary variables is not easy to find in practice. In fact, the auxiliary variables cannot be provided by survey data since the data is subject to sampling errors. Hence, it is of interest to the researchers to understand how to use the auxiliary variables which are based on survey data in small area estimation. Several studies on small area estimation models with measurement error have been conducted recently and they usually are based on types of measurement error assumptions namely functional and structural measurement errors. This paper reviews recent development of measurement errors in small area estimation. Illustrative examples are also provided using real data.