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Abstract:
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Assuming sample survey framework of two domains, one quantitative auxiliary variable with lognormal distribution, ratio-synthetic estimator was proved to be more efficient than BLUP under mixed model and unconditional inference. Similar results were obtained for sample surveys under unified model. In household surveys methods for estimation of total households and persons in domain of interest, which can be used for ratio-synthetic estimation in survey practice, were reviewed (Ghangurde, P.D.;JSM(2016)). In this paper the results on efficiency are extended to sample surveys in which post-stratification of sample units is done. For example, in a sample survey of retail trade sector with NAICS code 44711 value of annual sales is x-variable and employee salaries and wages is y-variable in the model; sample establishments are post-stratified as small (less than 100 employees) and medium (100 to 500 employees) using survey data. Efficiencies of ratio-synthetic estimator, assuming various sample sizes in domain, total sample size and values for parameters in the model, are obtained by unconditional inference assuming lognormal x-variable with unequal medians in post-strata.
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