Divide, Allocate et Impera: Comparing Allocation Strategies via Simulation

In stratified sampling, the problem of optimally allocating the sample size is of primary importance, especially when reliable estimates are required both for the overall population and for subdomains. To this purpose, in this paper we compare multiple standard allocation mechanisms. In particular, standard allocation methods are compared with an allocation method that has been recently adopted by the Italian National Statistical Institute: the Robust Optimal Allocation with Uniform Stratum Threshold (ROAUST) method. Standard allocation methods considered in this comparison are: (i) the optimal Neyman allocation, (ii) the multivariate Neyman allocation, (iii) the Costa allocation, (iv) the Bankier allocation, and (v) the Interior Point Non Linear Programming (IPNLP) allocation. Results show that the optimal Neyman allocation method outperforms the ROAUST method at the overall sample level, whereas the latter method performs better at the stratum level. Some results on the Nonlinear Programming method are particularly interesting.