Abstract
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.
Highlights
The overall sample size of a survey is usually designed to produce reliable estimates of parameters for the whole survey population and for some of its domains, where the reliability is understood as the acceptability of errors of the estimators
In the Lithuanian Labor Force Survey (LFS), the estimated errors of the domain-specific direct estimates of proportions of the unemployed are acceptable at the county level, but the accuracy of the direct estimates is poor at a lower municipality level
To get a deeper insight into differences among reliable estimators S, PK, DSC, HR, and FH, we present the distributions of their root mean squared errors (RMSEs) in the classes of domains
Summary
The overall sample size of a survey is usually designed to produce reliable estimates of parameters for the whole survey population and for some of its domains, where the reliability is understood as the acceptability of errors of the estimators. In the Lithuanian Labor Force Survey (LFS), the estimated errors of the domain-specific direct estimates of proportions of the unemployed are acceptable at the county level, but the accuracy of the direct estimates is poor at a lower municipality level. It seems that this problem can be solved by allocating the sample according to the subdivision by municipalities, but the total sample size is too large for the budget of the survey.
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