Estimation for small areas in household surveys

In many socio-economic surveys the objective is estimation of total or proportion of persons with a particular attribute. Multi-stage area samples are drawn from geographic strata and population within areal units is used as an auxiliary variable in ratio estimation. For large administrative areas, the auxiliary variable totals are available as population projections based on the last census. However, for small areas population changes are significantly affected by non-demographic factors and hence projections with high enough reliability are not available for small areas. In such situations the efficiency of design-based estimators for small areas can be improved by a ratio adjustment based on the auxiliary variable total for a large area. An inequality on the efficiency of the ratio adjusted estimator is established and its bias and variance is investigated