Sampling Allocation Strategies: A Simulation-Based Comparison

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 (Chiodini et al., 2008; Chiodini et al., 2011; Istat, 2017). 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. The ROAUST method is an extension of the Neyman allocation with a lower bound on the stratum sample size. Being n the overall sample size, with ROAUST the sample size in each stratum h is given by: ! = !" + ! !!!!!!!!!!!!. [1] In [1], n1h=n1/H, with H being the total number of strata, n1=αn, n2=n-n1, ! is the stratum population size and ! is the stratum standard deviation. α is a tuning parameter ranging from 0 (when the Neyman optimal allocation is obtained) to 1 (when the uniform allocation is obtained). Comparisons among these methods are carried out on the stratified sampling plan of the Italian Business and Consumer Survey, and performed in estimating the grand mean and the strata means ! of persons employed through Monte Carlo simulation. Results show that the optimal Neyman allocation method outperforms the ROAUST method at the overall level, whereas ROAUST performs better at the stratum level.