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Abstract:
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Assuming sample survey framework of two domains, domain of interest Ui and complementary domain Uc in sample design strata, unequal unit error variances proportional to auxiliary variable values, an assumption appropriate in household surveys, ratio-synthetic estimator was proved to be more efficient than BLUP estimator. Two components of approximate efficiency of ratio-synthetic estimator were derived, assuming known domain population totals or auxiliary variable totals (Ghangurde,P.D.(2014)). In this paper unit error variances are assumed to be equal, an assumption appropriate in most other sample surveys. Approximate efficiency of ratio-synthetic estimator is derived by unconditional analysis. The results in the case of sample surveys under unified model are similar to those in earlier paper. Approximate efficiency under two models are compared assuming that auxiliary variable has lognormal distribution. Ratio-synthetic is more efficient than BLUP in sample surveys under standard regression model assuming unequal or equal unit error variances; it is simple to use as compared to BLUP. Some applications in survey practice and methods to obtain domain totals and means are reviewed.
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