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Composite Estimators for Small Area Estimation (Method)

Summary

In surveys conducted by statistical offices one of the main problems is to have reliable estimates for domains for which the sample size is too small or even equal to zero. It is the consequence of the fact that many institutions need more detailed information not only for the whole country but also for some specific subdomains such as geographic areas or other cross-sections. It also concerns business statistics where increasing demand exists for information for different classification of activities (e.g., trade, manufacturing, transport, construction, etc.) including small, medium and large enterprises and many variables (e.g., revenue, operating costs, taxes, etc.). In such situations direct estimates based only on specific domain sample data are insufficient because of high variability and small precision. The remedy could be the methodology of small area estimation (SAE ) which plays an important role in the field of modern information provision, which aims to cut survey costs while lowering the respondent burden.

Thanks to their properties, SAE methods enable reliable estimation at lower level of spatial aggregation and with more specific domains, where direct estimation techniques display too much variance. Another advantage over direct estimators is that small area estimation can be used to handle cases with few or no observations for a given domain in the sample. Therefore it is necessary in many situations to use indirect estimates that borrow strength by taking into account values of the variables of interest from related areas and from that point of view increasing the “effective” sample size.

Generally speaking there are basically two types of indirect estimators: the synthetic and the composite estimators which can be derived under a design-based approach or taking into account the fact that an explicit area level or unit level model exists. In this part of the handbook only designbased composite estimators are described. For details on model-based composite estimators see Rao (2003) or the modules mentioned in section 24 below. The main aim of this module is to provide a set of principles for composite estimators. Information about the first group of estimators can be found in the module “Weighting and Estimation – Synthetic Estimators for Small Area Estimation”.

 

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