  We present a new method in problems where estimates are needed for finite
population domains with small or even zero sample sizes. In contrast to known
estimation methods, an auxiliary information is used to model sizes of
population units instead of a direct prediction of their values of interest. In
particular, via an additional characterization of regression models, we
incorporate a scatter and variabilities of the units sizes into an estimator,
and then it uses an information of the whole sample by taking into an account a
location of the estimation domain inside the population. To reduce an impact of
the introduced domain total estimator bias to the mean square error, we
construct also a regression type version of the estimator. An efficiency of the
method proposed is shown in a simulation study.
