Small area estimation techniques are used in sample surveys, where direct estimates for small domains are not reliable due to small sample sizes in the domains. We estimate the domain means by generalized linear compositions of the weighted sample means and the synthetic estimators that are obtained from the regression-synthetic model of fixed effects, based on the domain level auxiliary information. In the proposed method, the number of parameters of optimal compositions is reduced to a single unknown parameter, which is further evaluated by minimizing an empirical risk function. We apply various composite and related estimators to estimate proportions of the unemployed in a simulation study, based on the Lithuanian Labor Force Survey data. Conclusions on advantages and disadvantages of the proposed compositions are obtained from this empirical comparison.
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