Model-based confidence intervals in multipurpose surveys

SUMMARY The problem of calculating confidence intervals for finite population totals estimated using the ridge weighting procedure of Bardsley and Chambers (1984) is considered, and a robust model-based method proposed. Some empirical evidence on the performance of the method is provided. This shows the model-based approach is superior to more conventional methods of confidence interval estimation in this situation. Multipurpose surveys often lead to situations where the selected sample is unbalanced with respect to important benchmark variables. Model-based estimation techniques can provide a solution in the face of such problems. In the Australian Agricultural and Grazing Industries Survey (AAGIS), conducted annually by the Bureau of Agricultural Economics (BAE), the fitting of a linear model at the estimation stage of the survey results in the use of ridge-type sample weights which optimise the tradeoff between bias and variance for this situation. See Bardsley and Chambers (1984). A problem then presents itself as to an appropriate method of calculating confidence intervals for population means and totals estimated in this way. The next section develops the theory for such confidence interval estimation, based on the work of Royall and Cumberland (1978) and Obenchain (1977). An example of its use, and comparison with more conventional methods, is given in section 3. These results are discussed in section 4. 2. Theory The superpopulation model assumed for the AAGIS is fairly general, being based on the assumption that the target population for the survey can be divided into a number of statistically independent geographic regions. To simplify matters, we shall develop the theory for a single region, the extension to more than one being trivial. Let Y = (Y1, Y2,..., YN)T, where N is the population size, denote the N-vector of population values for a given survey variable. We assume