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CONCEPT OF SMALL AREA ESTIMATION Small area estimation methods are obviously used in the situations, where there is a need to “borrow strength” to determine the estimation using sample survey, but the sample of considered subpopulation isn’t large enough, what cause too large estimation error. Here “small area” can be understood as smaller administrative units (for example counties – in Polish poviats) or specific groups extracted from the population (for example specific socio-economic groups). This problem can concern also mini-domains or rare features, which are observed with smaller frequency and because of this, the estimates of such variables may cause difficulties even for larger administrative units (for example regions). SOURCES OF KNOWLEDGE RELATED TO THE SMALL AREA ESTIMATION The small area estimation methodology is systematically developed since 1980’s. Here we can mention books from J.N.K Rao (2003) N.T.Longford (2005) Mukhopadhyay (1998) In Polish literature you can also find some examples of more comprehensive studies of this topic. Here we can point out works by Bracha, Lednicki and Wieczorkowski (2003, 2004), Domański and Pruska (2001), Gołata (2004), Dehnel (2003) Żądło (2008). INDIRECT SMALL AREA ESTIMATION TECHNIQUES Synthetic estimation (ratio and regression) The synthetic estimator is applied to the specific domain/group it is assumed that the structure in the larger domain/group is similar to domain/group of interest. It is, however, biased Composite estimation To minimize the synthetic estimator bias one can use the composite estimation technique where the weighted average from the direct and synthetic estimator is used MODEL BASED ESTIMATION TECHNIQUES Empirical Best Linear Unbiased Predictor (EBLUP) Here mixed models theory is used involving fixed and random effects and small area parameters can be expressed as linear combination of these effects Empirical Bayes (EB) estimation In the EB approach the posterior distribution of the parameters of interest given the data is first obtained, assuming that the model parameters are known. The model parameters are estimated from the marginal distribution of the data and inferences are then based on the estimated posterior distribution Hierarchical Bayes (HB) estimation In the HB approach prior distribution of the model parameters is specified and the posterior distribution of the parameters of interest is than obtained . Inferences are based on the posterior distribution. Here, for example, value of considered parameter is obtained using posterior mean and its precision is obtained from the posterior variance APPLICATION OF SMALL AREA ESTIMATION TECHNIQUES TO POLISH HOUSEHOLD BUDGET SURVEY Models were obtained for regions (voivodships) and counties (poviats). For regions various income and expenditure models was prepared. For example model for available income was obtained using regional accounts data For counties also models for income variables was prepared. Here Polish Tax Register (POLTAX) for obtaining the auxiliary data was used
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