Introduction to Small Area Estimation

In this vignette we will describe an example on how to produce Small Area Estimates using different types of techniques. Different direct and model based estimators will be briefly described and their computation using the Rsoftware will be illustrated with a simulated data set. Small Area Estimation tackles the problem of providing reliable estimates of one or several variables of interest in areas where the information available on those variables is, on its own, not sufficient to provide a valid estimate. The information is usually collected by conducting a survey in some or all areas. The survey may involve the collection of information from the areas themselves or some of the individuals living in those areas, whose data are later used to provide area-based estimates. Direct estimators provide estimates based only on the local data (i.e., the data collected from the area itself) assuming that the sample is large enough, which seldom happens in practice. This problem is usually overcome by borrowing strength from other areas, usually neighbours or observations in the same area recorded at different times. Hence, model based estimators can be used to share information between different areas. In what follows, we will use Y i and X i to denote the area-level means of the target variable and covariate, respectively, and yi j and xi j to denote individual level values for subject j sampled from area i.