Small area estimation methods under cut-off sampling

Cut-off sampling is applied when there is a subset of units from the population from which getting the required information is too expensive or difficult and, therefore, those units are deliberately excluded from sample selection. If those excluded units are different from the sampled ones in the characteristics of interest, naïve estimators obtained by ignoring the cut-off sampling may be severely biased. Calibration estimators have been proposed to reduce the mentioned design-bias. However, the resulting estimators may have large variance when estimating in small domains. Similarly as calibration, model-based small area estimation methods using auxiliary information might decrease this bias if the assumed model holds for the whole population. At the same time, these methods provide more efficient estimators than calibration methods for small domains. We analyze the properties of calibration and model-based procedures for estimation of small domain characteristics under cut-off sampling. Our results confirm that the model-based estimators reduce the bias due to cut-off sampling and perform significantly better in terms of mean squared error.