Stratification and Allocation for Estimating a Complex Statistic Using Auxiliary Data

In the literature, methods for creating strata, identifying take-all units and allocating samples generally seek to minimize the variance under a fixed cost or to minimize the costs under a fixed variance in estimating a total. For a complex statistic that corresponds to a smooth function of total, such as a ratio or a regression coefficient, a sample design based on the total of one of the variables involved in the statistic is not necessarily optimal. We propose using a Taylor linearization to build an auxiliary variable to identify take-all units, generate strata and allocate the sample. Then, we use the usual stratification and allocation methods to minimize the variance of the estimator or the size of the sample. A simulation study is used to measure the method’s efficiency.