Business surveys carried out by National Statistical Institutes are usually aimed to obtain estimates of target parameters, e.g., the overall amount of industrial turnover for the whole population of business enterprises. Analogous parameters are usually defined with respect to relevant population sub-sets, i.e., sub-populations corresponding to geographical partitions (e.g., administrative areas) or subpopulations associated to economic cross-classification (e.g., enterprise size and sector of activity). An example is given by the estimation of the industrial turnover for each administrative region (e.g., NUTS2 level), or for each sector of activity (e.g., 2-digit NACE ). An estimator of the parameter of interest for a given sub-population is said to be a direct estimator when it is based only on sample information from the sub-population itself. Unfortunately, for most of surveys the sample size is not large enough to guarantee reliable direct estimates for all the sub-populations. A ‘small area’ or ‘small domain’ is any sub-population for which a direct estimator with the required precision is not available. Even though the term ‘small domain’ may seem to be proper in the business survey context, ‘small area’ is intended in the literature as a general concept and it is used to indicate a general partition of the population according to geographical criteria or other structural characteristics (socio-demographic variables for household surveys or economic variables for business surveys). In the following we will utilise preferably the term small domain but the term small area will be used too in its wide and meaningful definition.
When direct estimates cannot be disseminated because of unsatisfactory quality, an ad hoc class of methods, called small area estimation (SAE ) methods, is available to overcome the problem. These methods are usually referred as indirect estimators since they cope with poor information for each domain borrowing strength from the sample information belonging to other domains, resulting in increasing the effective sample size for each small area.
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