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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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