Authors:Maria Guadarrama (Department of Statistics, Universidad Carlos III de Madrid.) (Speaker) Isabel Molina (Department of Statistics, Universidad Carlos III de Madrid)Yves Tillé (Institut de Statistique, Université de Neuchâtel)
The OECD defines cut-off sampling as a sampling procedure in which a predetermined threshold is established with all units in the population and all units at or below (above) the threshold are excluded from the possible selection in a sample. This sampling technique is typically used in business surveys, in which small firms are included in the non-take stratum due to difficulty of getting information from those firms. Under a cut-off sampling procedure, it is not possible to compute design-unbiased estimators for linear parameters (e.g. means or totals) since the sample inclusion probabilities are zero for the discarded units. On the other hand, naïve estimators obtained by ignoring the cut-off sampling may be severely biased. Haziza et al. (2010) propose using auxiliary information to reduce the design-bias when estimating the population total; more concretely, they propose to use calibration and balanced sampling. However, the resulting estimators may have large variance when estimating in small areas. In the same line as calibration, model-based small area methods using auxiliary information might also help decreasing this bias if the assumed model holds for the whole population. At the same time, these methods provide more efficient estimators than calibration methods when estimating in small areas. In this work, we compare the performance of the calibrated estimators proposed by Haziza et al. (2010) with the empirical best linear unbiased predictor (EBLUP) and pseudo EBLUP for the estimation of small area domain means under cut-off sampling. Our results confirm that EBLUP under simple random sampling without replacement, and pseudo EBLUP under informative sampling, both samplings applied to the non-excluded units, help to reduce the bias due to cut-off sampling to a greater extent than calibrated estimators. They also perform significantly better in terms of mean squared error.
References:Haziza, D., Chauvet, G. & Deville, J.-C. (2010). Sampling estimation in presence of cut-off sampling. Australian & New Zealand Journal of Statistics 52, 303-319.